Question

A Christmas tree farmer planted 100 acres of trees five years ago. These trees now have a mean height of 80 inches with a standard deviation of 5 inches and follows a normal distribution.

a) Suppose one tree is picked at random. What is the probability that it will be less than 75 inches? Shade the region in the graph below that corresponds to the probability. Label the mean on the horizontal axis.

b) Suppose a random sample of 25 trees is selected and the mean height computed. What is the probability that it will be less than 75 inches? Shade the region in the graph below that corresponds to the probability. Label the center of the graph on the horizontal axis.

How would I solve this Via TI-84 calculator?

Answer 1

So let me solve this problem. Here is the solution:-

a)

The following is obtained graphically:

b)

The following information has been provided:

The following is obtained graphically:

In Ti84 calculator go to ->Probability->Normal distribution->Enter mean(80) and standard deviation(5)->Enter P(X<=75) and viola, you have the required answer-

Repeat the same for part b, just replacing the standard deviation by 1

Let me know in comments if anything is unclear. Will reply ASAP. Please upvote!