Question

The American Auto Association reports that the mean price per gallon of regular gasoline is $3.10, with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the likelihood the sample mean is greater than $3.08

Answer 1

0.65542

Explanation:

The formula for calculating a z-score when a random sample is selected is is z = (x-μ)/standard error

where

x is the raw score

μ is the population mean

Standard error = σ/√n

σ is the population standard deviation.

n = randomly selected sample

z = (x-μ)/standard error

z = (3.08 - 3.10) / 0.20/ √16

= -0.02/0.2/4

= -0.02/0.05

= - 0.4

Determining the Probability value from Z-Table:

P(x≤ 3.08) = P(<3.08)

P (z = -0.4)

= 0.34458

P(x>3.08) = 1 - P(x<3.08)

1 - 0.34458

= 0.65542

Therefore, the likelihood the sample mean is greater than $3.08 is 0.65542