Question

44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that

the average price is $3.82 per gallon and the population standard deviation is $0.33.

You decide to sample 40 convenience stores, collect their prices for a gallon of milk,

and compute the mean price for the sample.

What is the probability that the difference between the sample mean and the population

mean is less than $0.01? Please explain in details.

Answer 1

Solution :

Given that,

mean = = 3.82

standard deviation = = 0.33

n = 40

=

= / n = 0.33/ 40 = 0.05218

P( 3.81 < < 3.83) = P((3.31 - 3.82) / 0.05218<( - ) / < (3.83 - 3.82) / 0.05218))

= P( -0.19< Z < 0.19)

= P(Z < 0.19) - P(Z < -0.19) Using z table,

= 0.5753 - 0.4247

= 0.1506

The probability that the difference between the sample mean and the population

mean is less than $0.01 is 0.1506