The heights of pecan trees are normally distributed with a m

The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.

a) What is the probability that a randomly selected pecan tree is between 10 and 12 feet tall?
b) Find the 3rd quartile of the pecan tree height distribution.
c) If a random sample of 100 pecan trees is selected, what is the standard deviation of the sample mean?

Solution

(a) P(10<X<12) = P((10-10)/2 <(X-mean)/s <(12-10)/2)

=P(0<Z<1) = 0.3413 (from standard normal table)

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(b) P(X<x)=0.75

--> P(Z<(x-10)/2) =0.75

--> (x-10)/2 = 0.67 (from standard normal table)

So x= 10+0.67*2=11.34

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(c) So standard deviation of the sample mean = s/vn

=2/sqrt(100)

=0.2