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

Here we use Ti - 83 or Ti -84 calculator

Here we have given the "normal distribution "

X : Be the height of peacan tree .

a )

Follow the path of Ti - 83/84 calculator

Press "2ND " ...........>Press "VARS " .........>Select "normalcdf"

Lower : 8

Upper : 13

Press "enter"

Round above probability to 4 decimal place

Final answer for "a" part

Probability that a randomly selected pecan tree is between 8 and 13 feet tall = 0.7745

b )

We have given the 80^th percentile

This means we have 80% area to the left of Pecan tree Height

area = 0.80 (we convert 80% area into decimal )

Follow the path of Ti -83/84

Press "2ND " ...........>Press "VARS " .........>Select "invNorm"

Area = 0.80

Press "Enter "

From Ti -83/84 calculator we get

The pecan tree height = 11.68324247

We round the above value to 2 decimal place

The pecan tree height = 11.68

Final answer:-

The pecan tree height = 11.68

C )

To get answer for "a " and "b" we use the calculator Ti-83 or Ti -84

For a part the steps are

Press "2ND " ...........>Press "VARS " .........>Select "normalcdf"

For b part

Press "2ND " ...........>Press "VARS " .........>Select "invNorm"