Will someone please answer question 8.4 letters A through C and show all of your

Question

Will someone please answer question 8.4 letters A through C and show all of your work please. Thank you

between 32 mm and 42 mm? 8.4 Answer the following questions based on a population of bluegills with a known mean length of 152.09 mm and a standard deviation being 19.62 mm. a. What is the probability that any individual sampled at random from this population would have a length of 140 mm or shorter? b. What is the probability that a random sam- ple of 25 fish have a mean length of 140 mm or shorter? c. What is the probability that any individual sampled at random will have a length between 148 mm and 160 mm?

Explanation / Answer

Formula : Z = (X - Mean)/Std. dev.

a) P(X <= 140) = P(Z < (140 - 152.09)/19.62) = P(Z < -0.6162) = 0.2689

b) standard error, s = 19.62/sqrt(25) = 3.924
P(x_bar <= 140) = P(Z < (140 - 152.09)/3.924) = P(Z < -3.0810) = 0.0010

c) P(148 < X < 160) = P(X < 160) - P(X < 148) = P(Z < (160-152.09)/19.62) - P(Z < (148-152.09)/19.62)
= P(Z < 0.4032) - P(Z < -2085) = 0.6566 - 0.4174 = 0.2392

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