Hello I would like some help with my statistics studywork I

Hello. I would like some help with my statistics studywork. I have a horrible stat textbook. It goes into such little detail, and merely throws out letters and numbers with no specified instructions for calculating. So if you answer, please don\'t just put a formula, etc. with no explanation. Thanks!

1. Assuming that the heights of boys in a high-school basketball tournament are normally distributed with mean 80 inches and standard deviation 2 inches.

a. How many boys in a group of 40 are expected to be taller than 84 inches?

b. What percentage of boys fall between 78 and 84 inches?

c. What percentage of boys fall below 82 inches?

Solution

a. How many boys in a group of 40 are expected to be taller than 84 inches?

The probability that is taller than 84 inches is

P(X>84) = P((X-mean)/s >(84-80)/2)

=P(Z>2) = 0.0228 (from standard normal table)

So n=40*0.0228 =0.912

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b. What percentage of boys fall between 78 and 84 inches?

P(78<X<84) = P((78-80)/2<Z<(84-80)/2)

=P(-1<Z<2) =0.8186 (from standard normal table)

i.e. 81.86%

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c. What percentage of boys fall below 82 inches?

P(X<82) = P(Z<(82-80)/2)

=P(Z<1) =0.8413 (from standard normal table)

i.e. 84.13%