According to the Bureau of Labor Statistics, it takes an average of 22 weeks for

Question

According to the Bureau of Labor Statistics, it takes an average of 22 weeks for someone over the age of 55 to find a new job, compared with 16 weeks for younger workers (Source: The Wall Street Journal, September 2, 2008). Assume that the probability distributions are normal and that the standard deviation is 2 weeks for both distributions. a. What is the probability that it takes a worker over the age of 55 more than 19 weeks to find a job? b. What is the probability that it takes a younger worker more than 19 weeks to find a job? c. What is the probability that it takes a worker over the age of 55 between 23 and 25 weeks to find a job? d. What is the probability that it takes a younger worker between 23 and 25 weeks to fin a job?

Explanation / Answer

Let X be the random variable that number of weeks takes a worker over the age of 55.

let Y be the random variable that number of weeks takes a younger worker.

Given that X ~ N(mean = 22 weeks, sd = 2 weeks)

Y ~ N(mean = 16 weeks, sd = 2 weeks)

a) What is the probability that it takes a worker over tha age of 55 more than 19 weeks to find a job.

That is here we have to find the P(X > 19 weeks).

P(X > 19) = 1 - P(X 19).

Convert x=19 into z-score.

z = (x - mean) / sd

z = (19 - 22) / 2 = -1.5

That is now we have to find P(Z > -1.5).

This probability we can find by using EXCEL.

syntax :

=NORMSDIST(z)

where z is test statistic value.

P(Z -1.5) = 0.0668

P(Z > -1.5) = 1 - 0.0668 = 0.9332

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b) What is the probability that it takes a younger worker more than 19 weeks to find a job?

That is here we have to find the P(Y > 19 weeks).

P(Y > 19) = 1 - P(Y 19).

Convert y=19 into z-score.

z = (x - mean) / sd

z = (19 - 16) / 2 = 1.5

That is now we have to find P(Z > 1.5).

This probability we can find by using EXCEL.

syntax :

=NORMSDIST(z)

where z is test statistic value.

P(Z 1.5) = 0.9332

P(Z > 1.5) = 1 - 0.9332 = 0.0668

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c) What is the probability that it takes a worker over the age of 55 between 23 and 25 weeks to find a job?

That is here we have to find P(23 < X < 25).

First convert x=23 and x=25 into z-score.

z = (23 - 22) / 2 = 0.5

z = (25 - 22) / 2 = 1.5

That is now we have to find P( 0.5 < Z < 1.5).

P(0.5 < Z < 1.5) = P(Z 1.5) - P(Z 0.5)

= 0.9332 - 0.6915

P(0.5 < Z < 1.5) = 0.2417

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d) What is the probability that it takes a younger worker between 23 and 25 weeks to find a job?

That is here we have to find P(23 < Y < 25).

First convert y=23 and y=25 into z-score.

z = (23 - 16) / 2 = 3.5

z = (25 - 16) / 2 = 4.5

That is now we have to find P( 3.5 < Z < 4.5).

P(3.5 < Z < 4.5) = P(Z 4.5) - P(Z 3.5)

= 1.0000 - 0.9998

= 0.0002

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