Please explain your reasoning behind your answers I wil

Please explain your reasoning behind your answers! I will give 5 stars to the person who gives accurate answers AND thorough explanations!



Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.6 and standard deviation 0.79.



at most 3.00    
between 2.6 and 3.00    

Solution

z = x – m / (sd / sqrt(n) )

a)

i) P(x < 3) = P(z < (3 – 2.6) / (0.79 / sqrt(25) ) ) = P(z < 2.53) = 0.9943

ii) P(2.6 < x < 3) = P( (2.6 – 2.6) / (0.79 / sqrt(25)) < z < 2.53 ) = P(0<z<2.53)

= P(z < 2.53) – P(z<0) = 0.9943 – 0.███████ = ███████████

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

=&███; █(█ &███; (██ &#█████████; ███████) ██ (████████ █ ████████(█) ) ) &████; ███(█ &██████; ██████████) { ██ ██████████ ████████ ██ = █████████ ████ █████████ }

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

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

=&███; █ &██████; ███████

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