Question

According to the bureau of labor statistics, it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers. 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 find a job?

Answer 1

A) The Z score for a normal distribution is calculated as follows

Z = ( 19 - 22) 2

Z = -1.5

Probability that it takes a worker over the age of 55 to find jobs in 19 weeks = .06681

Probability that it takes a worker over the age of 55 to find jobs in more than 19 weeks = 0.5 - .06681

Probability that it takes a worker over the age of 55 to find jobs in more than 19 weeks = 0.43319

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B) Z = (19 - 16) 2

Z = 1.5

Probability that it takes the younger worker more than 19 weeks to find a job = (1 - 0.93319)

Probability that it takes the younger worker more than 19 weeks to find a job = 0.06681

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C) Probability that it takes a worker over the age of 55 about 23 weeks to find a job

Z = (23 - 22) / 2

Z = 0.5

Probability that it takes a worker over the age of 55 about 23 weeks to find a job = .69146

Probability that it takes a worker over the age of 55 about 25 weeks to find a job

Z = (25 - 22) / 2

Z = 1.5

Probability that it takes a worker over the age of 55 about 25 weeks to find a job = .93319

Probability that it takes a worker over the age of 55 between 23 weeks and 25 weeks to find a job = (0.93319 - .69146)

Probability that it takes a worker over the age of 55 between 23 weeks and 25 weeks to find a job = 0.24173

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D)

Probability that it takes a younger worker 23 weeks to find a job

Z = ( 23 - 16) / 2

Z = 3.5

Probability that it takes a younger worker 23 weeks to find a job = .99977

Probability that it takes a younger worker 25 weeks to find a job

Z = (25 - 16) / 2

Z = 4.5

Probability that it takes a younger worker 25 weeks to find a job = 0.99997

Probability that it takes a younger worker between 23 and 25 weeks to find a job = 0.99997 - .99977

Probability that it takes a younger worker between 23 and 25 weeks to find a job = 0.0002