According to a Human Resources report, a worker in the industrial countries spen

Question

According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 26 minutes.

a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be?

b. If the distribution of time spent on the job is approximately bell shaped, between what two times would 95% of the figures be?

c. If the distribution of time spent on the job is approximately bell shaped, between what two times would 99.7% of the figures be?

d. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 361 and 477 minutes? use %.

e. Suppose a worker spent 400 minutes on the job. What would that worker’s z score be, and what would it tell the researcher?
z score =

Explanation / Answer

Mean is 419 and s is 26

a) for 68% confidence , z is 1, thus lower limit is mean-z*s or 419-1*26 =393 and upper limit is 419+1*26=445

b) for 95% confidence is z=2 thus lower limit is 419-2*26=367 and upper limit is  419+2*26=471

c) for 99.7% confidence is z=3, thus lower limit is 419-3*26=341 and upper limit is 419+3*26=497

d) P(361<x<477)=P((361-419)/26<z<(477-419)/26)=P(-2.23 <z<2.23) thus it is 2*P(z<2.33)-1. from normal distribution table we get 2*0.9901-1 =0.9802

e) z score is (x-mean)/s = (400-419)/26 =-0.73

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