Question

According to American Automobile Association, the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65. Assume that the standard deviation of such cost is $0.25. Suppose that a random sample of n=100 gas stations is selected from the population and the cost per gallon of regular unleaded fuel is determined for each. What is the approximate probability that the sample has a mean fuel cost between $3.60 and $3.70?

Group of answer choices

0.9772

0.9544

1

0.1586

Answer 1

Solution :

Given that ,

mean =   = $3.65

standard deviation = =$0.25

n = 100

= 3.65

=  / n= 0.25/ 100=0.025

P($3.60<     <$3.70 ) = P[(3.60-3.65) /0.025  < ( - ) /   < (3.70-3.65) /0.025 )]

= P(-2 < Z <2 )

= P(Z <2 ) - P(Z <-2)

Using z table

=0.9772-0.0228

=0.9544

probability= 0.9544