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 $29 and the estimated standard deviation is about $9. (a) Consider a random sample of n = 130 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? The sampling distribution of x is not normal.The sampling distribution of x is approximately normal with mean μx = 29 and standard error σx = $0.07. The sampling distribution of x is approximately normal with mean μx = 29 and standard error σx = $9.The sampling distribution of x is approximately normal with mean μx = 29 and standard error σx = $0.79. Is it necessary to make any assumption about the x distribution? Explain your answer. It is necessary to assume that x has an approximately normal distribution.It is not necessary to make any assumption about the x distribution because μ is large. It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because n is large. (b) What is the probability that x is between $27 and $31? (Round your answer to four decimal places.)

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

See similar textbooks

Related questions

Concept explainers

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 $29 and the estimated standard deviation is about $9.

(a) Consider a random sample of n = 130 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?

The sampling distribution of x is not normal.The sampling distribution of x is approximately normal with mean μ_x = 29 and standard error σ_x = $0.07. The sampling distribution of x is approximately normal with mean μ_x = 29 and standard error σ_x = $9.The sampling distribution of x is approximately normal with mean μ_x = 29 and standard error σ_x = $0.79.

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

It is necessary to assume that x has an approximately normal distribution.It is not necessary to make any assumption about the x distribution because μ is large. It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because n is large.

(b) What is the probability that x is between $27 and $31? (Round your answer to four decimal places.)

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions