Question

The cost of 5 gallons of ice cream has a standard deviation of 7 dollars with a mean of 25 dollars during the summer. What is the probability that the sample mean would differ from the true mean by greater than 2.2 dollars if a sample of 83 5-gallon pails is randomly selected?

Answer 1

0.000221

Explanation:

Using the z score formula when a random number of samples is given =

z = (x-μ)/σ/√n, where

x is the raw score

μ is the population mean

σ is the population standard deviation = 7

n is random number of samples = 83

Note that:2.2 dollars = x-μ

z = 2.2/7/√8.3

z = 3.51402

Probability value from Z-Table:

P(x<27.7) = 0.99978

P(x>27.7) = 1 - P(x<27.7) = 0.00022069

Approximately = 0.000221

Hence, the probability that the sample mean would differ from the true mean by greater than 2.2 dollars if a sample of 83 5-gallon pails is randomly selected is 0.000221