An economist would like to estimate the mean amount of money that a family spends to within $45. If the amount spent by a family is considered to be normally distributed with a standard deviation of $190, what sample size would be necessary to be 93% confident?

An economist would like to estimate the mean amount of money that a family spends to within $45. If the amount spent by a family is considered to be normally distributed with a standard deviation of $190, what sample size would be necessary to be 93% confident?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An economist would like to estimate the mean amount of money that a
family spends to within $45. If the amount spent by a family is considered
to be normally distributed with a standard deviation of $190, what sample
size would be necessary to be 93% confident?

Expert Solution

Step 1

$Given Margin of Error (E) - 45 standard deviation (σ) = 190 α = 1 - 0.93 = 0.07 \frac{α}{2} = 0.035 z_{\frac{α}{2}} = 1.8119 (from z table)$

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