Question

1. The American Auto Association reports the mean price per gallon of regular gasoline is $2, with a population standard deviation of $0.20. Assume a random sample of 25 gasoline stations is selected and their mean cost for regular gasoline is computed. Assume that the population distribution is normal distribution.

Required:

a. What is the standard error of the mean in this experiment?

b. What is the probability that the sample mean is between $1.98 and $2.1? What theorem is necessary to evaluate the above probability?   

c. What is the probability that the difference between the sample mean and the population mean is less than 0.01?

d. What is the likelihood the sample mean is greater than $2.1?

Answer 1

a) According to Central Limit theorem, the standard error of mean is computed here as:

Therefore 0.04 is the required standard error of mean here.

b) The theorem here to be used is Central limit theorem. The probability that the sample mean is between $1.98 and $2.1 is computedhere as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.6853 is the required probability here.

c) The probability required here is:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.1974 is the required probability here.

d) The probability here is computed as:

Getting it from the standard normal tables we get here:

Therefore 0.0062 is the required probability here.