In a grocery parking lot 32 of 136 cars selected at random...

Name: Problem 33, Chapter 8: Applied Statistics in Business and Economics
Uploaded: 2025-07-27T23:32:18-08:00
Duration: 1 min
Channel: Nick Johnson
Description: In a grocery parking lot 32 of 136 cars selected at random were white. (a) Construct a 99 percent confidence interval for the true proportion of white cars. (b) May normality be assumed? Explain.

In a grocery parking lot 32 of 136 cars selected at random were white. (a) Construct a 99 percent confidence interval for the true proportion of white cars. (b) May normality be assumed? Explain.

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Key Concepts

Normal Approximation of the Binomial Distribution

This concept refers to the use of the normal distribution to approximate the binomial distribution when certain conditions are met, specifically when the sample size is large enough such that both np and n(1-p) are at least 10. This approximation allows for easier computation of confidence intervals and hypothesis tests since the binomial distribution can be cumbersome to work with directly, and the normal model provides a suitable approximation under the central limit theorem.

Confidence Interval for a Proportion

This concept involves estimating the range within which the true proportion of a population characteristic lies, with a certain level of confidence. It is calculated using the sample proportion as a point estimate, and the margin of error is determined by the standard error of the proportion and the corresponding critical value from the standard normal distribution. The interval provides a measure of uncertainty around the sample estimate, indicating how close the sample proportion is likely to be to the true population proportion.

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