Question

During a certain week​ (many years​ ago) the mean price of gasoline in California was ​$2.024 per gallon with a standard deviation of ​$0.053. A random sample of 47 gas stations was drawn from this population. What is the probability that the mean price of this sample was more than ​$2.042​? Show your work.

Probability​ = nothing ​(round answer to four decimal​ places)

Answer 1

Mean, = $2.024 per gallon

Standard deviation, = $0.053 per gallon

Sample size, n = 47

P( < A) = P(Z < (A - )/)

= = $2.024

=

=

= 0.00773

P(mean price of this sample was more than ​$2.042) = P( > 2.042)

= 1 - P( < 2.042)

= 1 - P(Z < (2.042 - 2.024)/0.00773)

= 1 - P(Z < 0)

= 1 - 0.5

= 0.5