Question

Please explain steps to find these answers on the TI 84 plus calculator:

A machine used to fill gallon sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The same mean of the cans is 127.9 ounces. Does the machine need to be reset? Explain your reasoning.

Answer 1

Solution:

Given: A machine used to fill gallon sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce.

Thus : Mean =

Standard Deviation =

Sample Size = n= 40

Sample Mean=

We have to determine whether machine need to reset or not.

We have two ways:

1) Find z score and check if lies within 2 standard deviation or outside 2 standard deviation from mean.

YES it is very unlikely that you would have randomly sampled 40 cans with a mean equal to 127.9 ounces because it Does not lie within 2 standard deviations of the mean of the sample means.

2) Using TI 84:

Step 1) Press STAT and select TESTS

Step 2) Select ZTest

Step 3) Select Stats and Enter Numbers

Thus z = -3.16

Since z = -3.16 < z = -2.00 , Thus machine need to reset.

YES it is very unlikely that you would have randomly sampled 40 cans with a mean equal to 127.9 ounces because it Does not lie within 2 standard deviations of the mean of the sample means.