Question: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of

Letxrepresent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of thexdistribution is about $40and the estimated standard deviation is about $9.

(a)

Consider a random sample ofn=60customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution ofx, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of thexdistribution?

The sampling distribution ofxis approximately normal with mean_x= 40 and standard error_x= $1.16.

The sampling distribution ofxis not normal.

The sampling distribution ofxis approximately normal with mean_x= 40 and standard error_x= $0.15.

The sampling distribution ofxis approximately normal with mean_x= 40 and standard error_x= $9.

Is it necessary to make any assumption about thexdistribution? Explain your answer.

It is necessary to assume thatxhas an approximately normal distribution.

It is necessary to assume thatxhas a large distribution.

It is not necessary to make any assumption about thexdistribution becausenis large.

It is not necessary to make any assumption about thexdistribution becauseis large.

(b)

What is the probability thatxis between $38and $42? (Round your answer to four decimal places.)

(c)

Let us assume thatxhas a distribution that is approximately normal. What is the probability thatxis between $38and $42? (Round your answer to four decimal places.)

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