Question

The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is the probability that a randomly selected pecan tree is between 8 and 13 feet tall? (round the answer to 4 decimal places)

(b) Find the 80th percentile of the pecan tree height distribution. (round the answer to 2 decimal places)

(c) To get the answers for part (a) and part (b), what technology did you use? If an online applet was used, list the URL and describe the steps. If a calculator or Excel was used, write out the function

Answer 1

By using excel we can solve this question easily.

Mean = $\mu$ = 10

Standard deviation = $\sigma$ = 2

a) We have to find the probability that a randomly selected pecan tree is between 8 and 13 feet tall.

That is we have to find P( 8 < X < 13)

P( 8 < X < 13) = P(X < 13) - P(X < 8) = 0.7745

( Using excel =NORMDIST(13,10,2,1)-NORMDIST(8,10,2,1))

b) We have given P(X < x) = 0.80

And we have to find value of x.

x = 11.68

So the 80th percentile of the pecan tree height is 11.68

( Using excel =NORMINV(0.8,10,2))

c) For findig part (a) and part (b) excel technology we had use.

For part a) excel command =NORMDIST(13,10,2,1)-NORMDIST(8,10,2,1)

For part b) excel command =NORMINV(0.8,10,2)