A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 13.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 13.3 weeks and that the population standard deviation is 8.5 weeks. Suppose you would like to select a random sample of 198 unemployed individuals for a follow-up study.Find the probability that a single randomly selected value is between 12.3 and 12.9.P(12.3 < X < 12.9) = Find the probability that a sample of size n=198n=198 is randomly selected with a mean between 12.3 and 12.9.P(12.3 < M < 12.9) = ### Probability and Statistics in Workforce StudiesA leading magazine, for instance, Barron's, reported that, at one time, the average duration of unemployment for an individual is 13.3 weeks. For the entire population of unemployed persons, assume the mean length of unemployment is indeed 13.3 weeks, with a standard deviation of 8.5 weeks. Consider selecting a random sample of 198 unemployed individuals for a follow-up study.**Problems:**1. **Single Randomly Selected Value Probability** Calculate the probability that a single, randomly chosen value falls between 12.3 and 12.9 weeks. \[ P(12.3 < X < 12.9) = \_\_\_\_ \]2. **Sample Mean Probability** Determine the probability that a sample of size $ n = 198 $ is randomly chosen, with a mean ranging between 12.3 and 12.9 weeks. \[ P(12.3 < M < 12.9) = \_\_\_\_ \] ### ExplanationIn both problems, you are dealing with normally distributed variables due to the Central Limit Theorem. For a single data point, the calculation involves using the standard normal distribution. When dealing with the sample mean, consider that the standard deviation becomes smaller, as it is divided by the square root of the sample size, n.This analysis is crucial in understanding statistical deviations from the average durations of unemployment in economic studies.

a. It is given that the number of weeks an individual is unemployed follow normal distribution with…

Answered: A leading magazine (like Barron's)…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 13.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 13.3 weeks and that the population standard deviation is 8.5 weeks. Suppose you would like to select a random sample of 198 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 12.3 and 12.9.
P(12.3 < X < 12.9) =

Find the probability that a sample of size n=198n=198 is randomly selected with a mean between 12.3 and 12.9.
P(12.3 < M < 12.9) =

### Probability and Statistics in Workforce Studies

A leading magazine, for instance, Barron's, reported that, at one time, the average duration of unemployment for an individual is 13.3 weeks. For the entire population of unemployed persons, assume the mean length of unemployment is indeed 13.3 weeks, with a standard deviation of 8.5 weeks. Consider selecting a random sample of 198 unemployed individuals for a follow-up study.

**Problems:**

1. **Single Randomly Selected Value Probability**

Calculate the probability that a single, randomly chosen value falls between 12.3 and 12.9 weeks.

\[
P(12.3 < X < 12.9) = \_\_\_\_
\]

2. **Sample Mean Probability**

Determine the probability that a sample of size $ n = 198 $ is randomly chosen, with a mean ranging between 12.3 and 12.9 weeks.

\[
P(12.3 < M < 12.9) = \_\_\_\_
\]

### Explanation

In both problems, you are dealing with normally distributed variables due to the Central Limit Theorem. For a single data point, the calculation involves using the standard normal distribution. When dealing with the sample mean, consider that the standard deviation becomes smaller, as it is divided by the square root of the sample size, n.

This analysis is crucial in understanding statistical deviations from the average durations of unemployment in economic studies.

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