Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $23 and the estimated standard deviation is about $9. (a) Consider a random sample of n = 40 customers, 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 of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? a)The sampling distribution of x is not normal. b)The sampling distribution of x is approximately normal with mean μx = 23 and standard error σx = $9. c)The sampling distribution of x is approximately normal with mean μx = 23 and standard error σx = $1.42. d)The sampling distribution of x is approximately normal with mean μx = 23 and standard error σx = $0.23. C is the correct answer Is it necessary to make any assumption about the x distribution? Explain your answer. a)It is not necessary to make any assumption about the x distribution because n is large. b)It is not necessary to make any assumption about the x distribution because μ is large. c) It is necessary to assume that x has a large distribution. d)It is necessary to assume that x has an approximately normal distribution. The correct ancswer is a ----------------------------------------------------------- (b) What is the probability that x is between $21 and $25? (Round your answer to four decimal places.) _? (c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $21 and $25? (Round your answer to four decimal places.) _? Answers needed for b and c

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $23 and the estimated standard deviation is about $9.

(a) Consider a random sample of n = 40 customers, 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 of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

a)The sampling distribution of x is not normal.

b)The sampling distribution of x is approximately normal with mean μ_x = 23 and standard error σ_x = $9.

c)The sampling distribution of x is approximately normal with mean μ_x = 23 and standard error σ_x = $1.42.

d)The sampling distribution of x is approximately normal with mean μ_x = 23 and standard error σ_x = $0.23.

C is the correct answer

Is it necessary to make any assumption about the x distribution? Explain your answer.

a)It is not necessary to make any assumption about the x distribution because n is large.

b)It is not necessary to make any assumption about the x distribution because μ is large.

c) It is necessary to assume that x has a large distribution.

d)It is necessary to assume that x has an approximately normal distribution.

The correct ancswer is a

-----------------------------------------------------------

(b) What is the probability that x is between $21 and $25? (Round your answer to four decimal places.) _____________?

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $21 and $25? (Round your answer to four decimal places.) _____________?

Answers needed for b and c

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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