Question

The cost of 5 gallons of ice cream has a variance of 49 with a mean of 37 dollars during the summer. What is the probability that the sample mean would be greater than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

mean = = 37

variance = ² = 49

standard deviation = = ² = 49 = 7

n = 77

= = 37

= / n = 7 / 77 = 0.798

P( > 35.2) = 1 - P( < 35.2)

= 1 - P[( - ) / < (35.2 - 37) / 0.798]

= 1 - P(z < -2.26)

Using z table,    

= 1 - 0.0119

= 0.9881