The lifetime of a supertough AAA battery is normally di

The lifetime of a supertough AAA battery is normally distributed with mean u=28.5 and standard deviation o\’ = 5.3 hours. FOr a battery selected at random, what is the probability that the lifetime will be 34 hours or more?

and between 25 and 34 hours?

Please show work

Solution

Question b ) between 25 and 34 hours

First we calculate for x < 25

P(x<25) = (x – xmean) / s.d

Where:
x = observed value
xmean = mean (28.5 hours)
s.d = standard deviation (5.3 hours)

P(x<25) = (x – smean) / s.d
███(██&█████;█████) = (██████ &#█████; ████████) ██ ████████
█(█&██;█████) = (███████████) ██ █████ = ██████████████

█████ ████████ █████████ ████ ██████████████████ █████████████ ██████████


████████████████████████████ ████ ██ ██████████████ ████ ███████████████ █████ █████████ ████ ██████████


█████ &#███████; █████████ = ████████ ███ █████████████


██████████████████ ██████ ████████████████████████ ████ ██ ███████████████ █████████████████ ████████ ████████ ████ ██████████ ██████ ███████████


███████████ ██(█████&███;██&████;█████) = (███ &#█████████; ████████ &#█████████; ███████) = ███████████ ██ ███████████

Assignment 8 Question 16 Find the amplitude for the fol

Assignment 8

Question 16

Find the amplitude for the following function:

a) 8

b) 52

c) 6

d) 5

e) 10

Find the period for the following function: f(x) = 5 sin (1/3 pi x + pi) + 3

Solution

f(x) = 5sin((1/3)pix + pi) +3

it is in the form of f(x) = Asin(██████ ███) + ██

█ = █████████████████

==&███; ██ = ███

█████████ ██

A conservationist wants to know if the average water le

A conservationist wants to know if the average water level in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at %u03B1 = 0.01

Horseshoe Lake
Swan Lake

Solution

Fisrt step :

Hypothesis :

Ho: Mean(Horseshoe Lake)=Mean(swan lake)

H1: Mean(Horseshoe Lake)>Mean(swan lake)


Second step:

Critical region:

Degree of freedom = 23+23-2 =44


T(0.01,44) =2.414


If Test Statistics>2.414. Then Reject the NULL Hypothesis.


████████ ███████:

████████:

████████████████=█ =████████ = ██

█████(███████████████████) =████████((██████)^███+(███████)^█)██████████(█████) = ████████████████████


███████████ ███████:

█=███████████████████████= ██████████████████


█████████████ ███████:

████ ███████████████&████;████████████ ███████ ██████████ ██████ █████████ █████████████████████

██████, ██████ ████████████████ ████████ ████████ ██████████████ ████████ ███████████ ████ ███████████████████ ████ ████ ██████████ █████████ ███ ███████████ ████████████ █████████████ ██████ ███████ █████████



Assignment 8 Question 14 Find the amplitude for the fol

Assignment 8

Question 14

Find the amplitude for the following function:

a) 59

b) 6

c) 109

d) 23

e) 518

Solution

f(x) = (5/9) sin((1/3)x)

it is in the form of f(x) = Asin(Bx ██) + ██

█ = ███████████████████

==&███; ███ = ██████

████████████ ███

Suppose a normal distribution has a true population mea

Suppose a normal distribution has a true population mean of 18 and a true standard deviation of 2. What % of obervations will be:

a.) 18 or less ___

b.) 18 or greater _____

c.) in the range from 16 to 20 ____

Please show work

Solution

a.) 18 or less ___=p(z<0)=50%

█████) ████ ███ █████████████████ █████████(█&█████;██)=██████

██████) ████ ███████ █████████ ███████ ████ ██ █████ ███████=██(████&███;█&███;██)=█████████████

ASSIGNMENT 04 Sources must be cited in APA format. Your

ASSIGNMENT 04

Sources must be cited in APA format. Your response should be four (4) double-spaced pages; refer to the \”Assignment Format\” page located on the Course Home page for specific format requirements.

Respond to the items below.

   •   Explain customer-perceived value.

   •   Explain total customer satisfaction.

   •   What valuable functions can brands perform for a firm?

   •   Given that the power of a brand resides in the minds of consumers and how it changes their response to marketing, there are two basic approaches to measuring brand equity. Briefly, describe each of these approaches.

   •   Incorporating the concepts discussed in this assignment, answer the following: How does a loyal brand community support the positioning and branding of a small business? Provide an example to support your explanation.

-End-

Solution

Perceived customer value is marketing and branding related concept that points out that success of a product is largely based on whether customers believe it can satisfy their needs. This phrase emphasizes that when a company develops its brand and markets its products, customers ultimately determine how to interpret and react to marketing messages. Companies spend significant time researching the market to get a sense of how customers think and feel.

Total customer satisfaction is a business strategy aimed toward ensuring that the overall customer experience is good, in addition to providing a quality product or service. This is particularly important when competitors offer similar or identical products or services for similar prices. The business that can provide the best overall experience will likely be more successful than the others simply because customers find conducting business there more satisfying overall. Adopting customer satisfaction as a primary business goal can sometimes be costly and difficult, but doing so is likely to pay off over time.

A business must, first of all, offer a good product or service if total customer satisfaction is to be achieved. Even if the customer is treated well and has an overall positive experience purchasing the product or service, he will probably not recommend or return to the business if the product is not satisfactory. A business must, quite simply, be good at providing the product or service that it offers or customers will not be satisfied overall.

A brand is a consistent, holistic pledge made by a company, the face a company presents to the world. A brand serves as an unmistakable and recognizable symbol for products and services. It functions as the “business card” a company proffers on the competitive scene to set itself apart from the rest. In addition to differentiating in this way, a brand conveys to consumers, shareholders, stakeholders, society and the world at large all the values and attitudes embodied in a product or company. A brand fulfills key functions for consumers and companies alike.

A brand fosters brand and customer loyalty. Particularly strong brands can establish the prevalence of premium prices on the market and soften consumer reactions to price changes. Specifically brand-oriented buyers – who are more concerned with brands than prices – are more resilient when it comes to changes in the competitive scenario. This decreased sensitivity to price changes makes them more valuable as customers.

The reduction in perceived purchasing risk lays the groundwork for a relationship of trust, giving brands a role to play in lashing customers to a company.

Brands can counter the swelling ranks of trade because dealers stock their shelves and fill their order lists with products explicitly requested by consumers. Strong brands in particular keep sales levels and market share constant and considerably lessen dependence on short-term special promotions.

A brand unlocks great potential in terms of licensing opportunities as well, helping companies achieve plans for international expansion.

Finally, brands also offer companies potential for honing a clear profile and overshadowing the competition. Strong brands in particular can reduce the risk that new product launches will flop and can be used as platforms for successful brand stretching (also in terms of launches in completely new product segments and sectors).

Brand equity is a phrase used in the marketing industry which describes the value of having a well-known brand name, based on the idea that the owner of a well-known brand name can generate more money from products with that brand name than from products with a less well-known name, as consumers believe that a product with a well-known name is better than products with less well-known names.

Brand equity refers to the value of a brand. In the research literature, brand equity has been studied from two different perspectives: cognitive psychology and information economics. According to cognitive psychology, brand equity lies in consumer’s awareness of brand features and associations, which drive attribute perceptions. According to information economics, a strong brand name works as a credible signal of product quality for imperfectly informed buyers and generates price premiums as a form of return to branding investments. It has been empirically demonstrated that brand equity plays an important role in the determination of price structure and, in particular, firms are able to charge price premiums that derive from brand equity after controlling for observed product differentiation.

Brand equity is strategically crucial, but famously difficult to quantify. Many experts have developed tools to analyze this asset, but there is no ██████████ ██████ ████ ████████████ ███████ ████ ████ ███ ██████ ████████████ ███████████████████ ██████ ███████████████████ ██████████████████████ █████████ █████████████████ ██████ ██████████ █████ ███████████████ ██ ███████████ █████████████, █████ ██████████████████████████ ██████████████ ████████████████████████ ████ ████████████████████████ █████████ █████████████ ███ █████████████████████████ ████ ████████████████████ ███████████████████████ ██████████████ ███████████ ███████████████ ██████████████████ ██████████████ ███████ ███ ███████████████ ██████████████ █████ █████████████ ████████, █████████ ████████ ███ ██████████████████ ████████████████████████ ██████████████████ ███████ ██ ██████████████████ ███████ ████████████████████████ ██████ █████████████████████ ████████████████, ████████ █████████████████████ ███████████████████████████ ██████████ █ ██████████ ████████████████ █████████████████ █████ █████████ █████████████ █████████████ ████ ████████ █████████████████ █████ ███ ███████████ █████ ██████████ █████ ██████████████ ███████████████ ████████████████, ████████████ ████ ██████████████ ████████████████ ███████ █████████ ███████████ ███ \&#████████;████████ ██████████████\&#██████████; ████████ █████████ ████████████

███████ ███████████ █████████████████ █████████████████ █████ ████████ ███████████████ ████████████████████ █████████████████ █████ ████████████ █████████████████ ██████ ███████████ █████ ██████████ █ █████████ ███████ █████████████████ █████████████ █████████████ ██████ █████████████ ██████ ███████ █████████████ ███████ ██████████████████ █████ ████ ██████████ ███ ██████████ █████ ████ ██████████ █████████████ ████ █████████████████ ██████████████████████ ██████ ██████ █████ ██████████████ ███████████ ████████████████ ███████████ █████ ██████ █████████████ ██████ ████████ ███████████ ███ ████ █████████████████ █████ ███████ ████ ██████ █████ ████████ █████████ █████ ████████ ██████████████████ ██████████████████████ █████████ ███████████ █████████ █████ ██████████████████████

█████ ██████████████ ████████ ██ █████████████████████████ ████████████ █████████ █████ ████████ █████ ███████ █████████ ██████ ██████████ ███████████ ████████ ████ ██████ █████████ ███████ ██████████ ████████ ████████████████████ ██████████████████ ██████████████████ — █████████████ ████████ ████████████ █████ ███████ ████████████████ █████████ ██████████████████ ████ ██ ████████████ — █████ ███████████ ████ ████████████ ██████████ ████ █████████████ ███████████ ████████████████████████████ █████ ███████ █████████ ██████ ██████████████, █████████████ ███████ ███████ ████████ ██████████████ ███████ ██████████ ██████ ███████████ ████████ █████████████████████████ █████████ ██████ ███████████████████████ ████████████████ ████ ████████████ █████████████ ████ ██████ ██████████ ███████ ██████ ███████ █████████ ███████████ ███████ █████████ ███ ████████████ ████████ ███████████████████ █████ ████████████████

█████████ ████ ███████████████ █████████ █████████████

████████ ███ ████████████ ████ ███████████████ ████████ ██████████████████ ███████████, ████████████████ ███████ ████████ ███ ██████ ██████████ ███ █████████████ ████ ██████████████ ████████ █████████████████ ███████ ███████████████ ███████ ██████ ████████████████████ ████ ████████ ██████████████████ ██████████ █████████ ███████████████████ ██████████████ ██████████████ ████████ ████████████████, ██████████████ █████ ██████ ██████████████████ ████████ █████ ████████████████████ ████████ █████ ██████ ███████████████

████████ ██████████████ ████████ █████████, ██████████ ██████ ██ ████ ███ ██████████████

████████ ████████ ████ █████ ██ █████ ███████████████████ ████████ ██████████████████████ ██████ ██████ ████ ██ ██████████████, █████████████ ████████ ███████████████ ███████ ██████████████ ██████ ██ ██████ █████ ██████ ███ ███████████ ███████████ ███████ ██████████████████████ █████████████████ ████ ██ █████████████ ██████ █████████████████ ███████████████████████, █████ █████ █████████████ ████████ ███████ ███ █████████ █████ ███████████ ███████ █████████ ███\&#███████;█ ████████████████ █████ ██\&#████████;█ ████████ ███████████ ███████ ███████████ █████████████ █████████ ████████ █████ ██████████████ ███, ███████ █████████ ██████\&#███████████;████ ████████████████ ███ ██████████ ████\&#██████████;██ █████████ ██████ █████ ████████ █████████████████████████████

███████████████ ████████ ███ ████████████████ ████████ ████████████████████

████████ ████████ █████ ███████████████ ████, ██████ ███ ██████ ██████████████ ███████ ██████ ████████ █████████ ███████████████ █████████ ██████████ █████████████ ████ █████████ ███████████████████ █████████ ██████████████████ █████████ █████████████████████████ ███████ ██████████ ███████ ███████████████████ ███ ████████████████████ █████ ████████ █████████████████████████████

█████████ ████ ████████ █████████████████ █████████████████████████ █████████ ███████ ████████████████████

██████’███ ██████████ ██ ███████ █████████████████████ ███ ███████████ ██████████████████████ ████████ ███████████ ███ ██████████ ██████████████████, ████████████ ██████ █████████ ██████████████ █████████████ — ████ ████████ ███ ████████ ███████████ ███ █████ █████ ███████ ████ ██████ █████████ ██████████ ███████████ █████ ███████ ████████

███████████ ██████ ███████████ ██████████████████ █████████ ███ ███████████████████████ ████████ ███ ████████████

████ █████████ ███████ █████████████████ █████ ███████████████████’ ██████████████ ████████ ████████████████ █████████ ████████████████ ████ ████████████████████ ███ █████████ ████████████ ███████████ ██ ███████████ █████████ █████ ██████████████████ ████ █████████████████

██████\&#█████████;█ ██████████████ ██████ ██████ ██████████████ ████ ██████ ███████ ██████ █████████ ██████ █████████ ██████████████

████████████████████████████, ████ █████ ███████ ██████ ███████ ███████████████████ ████████ ██████████████ ███ ████████████ █ ████████████ ████████████████████

████’██ ██████ ███ ███████████ ████████ ███████ ██ ██████████████ ██ █████ █████████████████

███████ ████████ █████████ ████ █████████ ███████ ██████████████████████ ███████████████████ ██████████ ████ ██ ███████ █████████████████ ██████████ ████████████ ██████████████████████████ █████████████████████████████, ██████ ███████████████ ███████████████ ████████ ███ █████ ██████████ █████ ███████████ ██ █████████████████████ █████████ █████ ████████████ ██████████ ████ ███████ █████████████ ███████ ██████████████████████ ████████████████ ███████ █████████████████ ██████████ ███████████ ████ ████████████████ ██████████████████ █████ █████ ████████████ ██████ ██████████████████ ███████████ ███████████████████ ██████ ██████████████, █████████ ████████████ █████ ██████ ██████████ ██████████ ████████████████████████

████ ████████████████████████, ██████████ ███████ ███████████████ – ███████████ █████████ ██████████████████ █████ █████████ █████

█████ ██████████ █████ ███████████████████████ ██████ █████████ ████████████ █████ ██████████████████████, ███████████████████ █████ ██████████ ████████ ████████████████ █████ ████████████████ ████ ██████ █████████████████████████ ██████████ ████ ███████████ █████████████████ ██████████ ██████████████ ██████ ██████████████████████████████████ ███████ █████████ ██████ ███████ ██████ ██████ █████ ███ █████████████ █████████ █████████ ██████████████

███████████████ ██████████████ ███████ ███████████████ ██████ █████████████████████████████ ██████ ████████████████

██████\&#███████;██ █████████ ███████ ███████████ ████ ████████████ █████████ █████████ ████████████████████████ █████████ █████████████████████████████ █████████████████████████ ████████ █████████████ ████████, ███████████████ ███████ ██████████████ ████████████ ███████████████████ ███████ ████ █████████████████████████ ██████ ███████████████████ ███████████ ███████████ ████████████████

█████████ █████ ███████ █████ ██████████████████ ██████ ████████ ███ ███████████████████████ ██████\&#███████████;███ ███████ ████

██████ ████████████████ █████ █████████████ ███ ████████ █████████ █████████████████ — ██████████████ ██████████ ██████████████████\&#████████; ██████████████████████ ██ ██████ ██████████████ ██████████████████ █████████ ██ ███████████████ ████████████████ ██████ ██████████████ ███████ ████████ ███████ █████ █████████ ██████ ███████ ██████████ ████████████ ████ ██████████████████████ ████████ ████ ████ ████████ █████ █████████████ █████████████████████████ ████ █████████████ ███ █████████████ ███████████ ██████████ ██████ ████████ █████ █████████████████████████

I havent taken any statistics, and Im totally doomed. P

I haven\’t taken any statistics, and I\’m totally doomed. Please help!!!

From a manufactory%u2019s production line, there are two types of soda products: Apple and Cherry flavors. Your job is to randomly select samples from the each product line and monitor the quality of the products from data you have measured. You have used the same protocol of analysis for both products. In an initial analysis, 535 samples of Apple soda and 653 samples of Cherry soda samples were analyzed. The mean and standard deviation of the density from Apple soda was found to be 1.27 g/ml and 0.15 g/ml, respectively. The standard deviation of densities from Cherry soda was found to have the same value as from Apple soda, probably due to the same protocol of analysis.

1. You will select a random sample of the Apple soda and measure its density tomorrow. What range of densities you expect the measurement will fall within at the 95% confident level?

2. You have measured the density of a random Cherry soda yesterday and found its value as 1.09 g/mL. Estimate the 95% confident interval of the mean for the entire population of Cherry soda from this single measurement.

3. You have measure 25 randomly selected Cherry samples from the production line today. The mean and standard deviation were found to be 1.05 g/ml and 0.35 g/ml, respectively. Estimate the 95% confident interval of the mean for the Cherry soda population again from the data of 25 samples.

4. Another technician had substituted for you when you took some time off. She has measured the densities of randomly selected 25 samples of Apple soda and determined the mean and standard deviation as 1.16 g/ml and 0.53 g/mL, respectively. Were the results of her measurements show the recent apple soda produced falls within the 95% confident interval of the initial production? Provide evidence for your answer.

5. From the result of your answer for question 4, comment on the reliability of test this technician run. Is the cause of the difference between her mean and the mean of the initial test indeterminate or determinate error?

Solution

1 ) 95 % CI = (1.27 – 1.96*0.15 / sqrt(535) , 1.27 + 1.96*0.15 / sqrt(535))

= (1.2573 , 1.2827)

2 ) 95% CI = ( 1.09 – 1.96*0.15/sqrt(653) , 1.09 + 1.96*0.15/sqrt(653))

= ( █████████████ , ████████ )

██ ) █████████ = ( ██████ &#████████; ██████*███████████████████(████) , ████████ + █████████*████████████████(███) )

= ( █████████████ , ████████████ )

Assignment 8 Question 13 Find the period for the follow

Assignment 8

Question 13

Find the period for the following function:

a) 35

b)

c) 103

d) 2

e) 4

Solution

Option (e)

f(x)=3/5 sin(x/2)

We know that the period of y = sin x is 2 Pi . In general, the period is (1/b)*(2 Pi).

Therefore, the ████████████ ██████ ███ = █████ (█████ ███) ████ [████(███████)]*(███ ████) █████ ██ ██████

███, ███████ ██████████████ ████ ███████████████ █(██) = █████ ███████(█████) ████ █ ███

██████████ (███)

When performing a hypothesis test, you must make an ass

When performing a hypothesis test, you must make an assumption in order to perform it. Assume that the hypothesis you are testing (the null hypothesis) is true. This assumption allows you to calculate the probability of the test results. You then use that probability to decide whether or not to accept the hypothesis and the claim associated with it. The more likely the results, the more readily you accept the hypothesis.

This kind of analysis can be used to evaluate any idea for which there are enough facts or data. For example, what about the premise that Jesus is the Son of God? Josh McDowell takes a similar approach to answering this question in his book, Evidence That Demands a Verdict (Campus Crusade for Christ, 1972).

In his book, McDowell collects a variety of information that attests to the Bible%u2019s validity and Jesus%u2019 claims to being the Son of God. He includes the interesting results of a large volume of research. In the section about messianic prophecy, he quotes the probabilistic analysis of Peter Stoner in Science Speaks (Moody Press, 1963).

Stoner used the assumption that Jesus was just a man and not the Son of God to perform a probability analysis and hypothesis test on some messianic prophecies. In this case the hypothesis was that Jesus was not the foretold Messiah or the Son of God. He then examined the probability of a selection of prophecies coming true if Jesus was in fact not divine.

Using a selection of 8 prophecies, Stoner showed that the probability of all 8 prophecies being fulfilled is 1 in 1017. Using the language of hypothesis tests, this means that you would reject the hypothesis that Jesus is not the Messiah for any %u03B1 > 10-17. To put it another way, %u03B1 > 0.00000000000000001. The smallest %u03B1 that is normally used for a hypothesis test is %u03B1 = 0.01. This means that you can safely reject the hypothesis that Jesus is not the Messiah or the Son of God.

For more on this, I recommend Josh McDowell%u2019s book Evidence That Demands a Verdict. Peter Stoner%u2019s work can be found in Science Speaks, published by Moody press. Stoner%u2019s book might be difficult to find, but McDowell%u2019s book, Evidence That Demands a Verdict is still in print.

The references for the 8 Old Testament prophecies that Peter Stoner analyzed are listed below along with the verse references for their fulfillment. It is likely that most students in this course believe that Jesus Christ is divine, so listing probabilities of Him doing certain things is irrelevant. However, what Stone is doing is playing the devil%u2019s advocate. He%u2019s saying to the skeptical, %u201COkay, let%u2019s have it your way for a second. If Jesus of Nazareth was just an ordinary man, what is the probability that he could fulfill all the prophecies by chance?%u201D

1.      Think more about the probability of each event. For example, what is the chance that a person born in Israel would be born in or be from Bethlehem? What would the probability be that a person would be crucified in Israel given that he lived in that time period? Put numbers on each of the eight prophecy fulfillments. Some of the probabilities will be subjective, but put values that you feel make sense and write a short justification for the value you picked. For example, if one of the prophecies said that the Messiah would come from the house of Judah, you could say that the probability is 1/12, since there were 12 tribes. Do not put probabilities of 0 or 1. You can get closer than you might think%u2014Google can tell you what the population of Israel was in the days or Christ, for example. The important thing is to write down your justification as to why you assigned the probabilities you did to each prophecy.

2.      Choose one of the eight prophecies in Stoner%u2019s research. Explain how he might have arrived at the probability he assigned. Do you think his estimated probability is too high(conservative) or too low? What probability would you assign and why?

3.      Given the new probabilities you associated with each prophecy, what is the probability that all eight happened in sequence? Hint: What%u2019s the probability that you flip a coin and it comes up tails? 50%. What if you flip the coin twice and it comes up tails both times? 1/2*1/2 = 25%. What if three times? 1/2*1/2*1/2 = 1/8. What if four? Five? Now think about the probability of just two prophecies coming to pass at the same time. What would the probability be? What about three prophecies? Eight? Show your work.

4.      Reflecion Question: Do you think it is possible that someone other than Jesus could have    fulfilled the prophecies of the Bible? Why do some religious groups claim to believe the Bible, but reject Jesus as the Messiah?

Solution

Just because we did not fail to reject the alternate hypothesis doesn\’t mean we fail to prove the null is true, that Jesus is NOT the Messiah(SoG). One can also reset your alpha to 0.000000000000000001(10^-18) and the outcome is now different. We have to accept the null. But with the same rea█████████, █████████████ ████ ████████████████ ███████ ████████████ █████████████████████ ( ██████████ ████ ████████ ████████████████) █████████ ████████ ██████████ ███████ ███████ ██████ █████████████ █████████████████ ██████ █████ ██████ ███ ██████ ███ ████████ █████ ██████ ██████████ █████ █████████ ████████████ ██████ ██████████, ██████ ████████████████ ███████ ████████████ ██ ██████████████ █████████ ███ █████████████, ██████████████████ ██████ ██████████ ████████ █████ █████ ███████████████████ ███████ ███████ ██████ ██████████████