Please explain your reasoning behind your answers so I am able to understand! I will give 5 stars to the person who gives both accurate answers AND provides thorough explanations!(:

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.5. (Round your answers to four decimal places.)

### Solution

z = x – m / (sd / sqrt(n) )

a) P(x>51) = P(z > (51 – 50) / (1.5 / sqrt(10) ) = P(z > 2.11) = 1 – P(z < 2.11) = 1 – █████████████ = █████████

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