Question

The cost of 5 gallons of ice cream has a variance of 49 with a mean of 36 dollars during the summer. What is the probability that the sample mean would differ from the true mean by less than 1.5 dollars if a sample of 142 5-gallon pails is randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 36

variance = 49

standard deviation = = 7

n = 142

= 36

= / n = 7 / 142

P(34.5 < < 37.5) = P((34.5 - 36) / 7 / 142 <( - ) / < (37.5 - 36) / 7 / 142 ))

= P(-2.55 < Z < 2.55)

= P(Z < 2.55) - P(Z < -2.55) Using z table,

= 0.9946 - 0.0054

= 0.9892

Probability = 0.9892