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 less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected

Answer 1

P ( Z < 35,2 ) = 0,0122 or 1,22 %

Explanation:

Assuming a normal distribution:

μ = 37

σ² = 49 σ = 7

Z(s) = ( x - μ ) / σ /√n

Z(s) = ( 35.2 - 37 ) / 7 / √77

Z(s) = - 1.8 * 8.77 / 7

Z(s) = - 2.25

From z- table we find the area under the bell shape curve and it is:

0,0122

Then P ( Z < 35,2 ) = 0,0122 or 1,22 %