Automatic teller machine receipts show that customer withdrawals have a skewed distribution with a mean of $72 and a standard deviation of $15.Let $y‾\overline{ y}$ represent the mean withdrawal for the next 200 customers at the machine.Describe the sampling distribution model of this mean.

A) The distribution is skewed with a mean of $72 and a standard deviation of $15.
B) N(72,15)
C) N(5.1,15)
D) N(72,1.41)
E) There is not enough information to describe the distribution.

Question

Automatic teller machine receipts show that customer withdrawals have a skewed distribution with a mean of $72 and a standard deviation of $15.Let

y‾\overline{ y}

represent the mean withdrawal for the next 200 customers at the machine.Describe the sampling distribution model of this mean.

A) The distribution is skewed with a mean of $72 and a standard deviation of $15.
B) N(72,15)
C) N(5.1,15)
D) N(72,1.41)
E) There is not enough information to describe the distribution.

Patrina Nicholson · Accepted Answer

Final Answer : D, Explanation :  The sampling distribution of the mean follows a normal distribution, where the mean of the sampling distribution is equal to the population mean (72) and the standard deviation of the sampling distribution is equal to the standard deviation of the population divided by the square root of the sample size (15/sqrt(200) = 1.41). Therefore, the correct answer is N(72,1.41).

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