Question

1.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 27 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?
enter the lower limit for the interval where 68% of the values would fall  to enter the upper limit for the interval where 68% of the values would fall   

b. If the distribution of time spent on the job is approximately bell shaped, between what two times would 95% of the figures be?
enter the lower limit for the interval where 95% of the values would fall  to enter the upper limit for the interval where 95% of the values would fall   

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?
enter the lower limit for the interval where 99.7% of the values would fall  to enter the upper limit for the interval where 99.7% of the values would fall   

d. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 358 and 480 minutes?
enter percentages rounded to 1 decimal place % (Round the intermediate values to 3 decimal places. Round your answer to 1 decimal place.)

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 = enter the z score rounded to 3 decimal places  (Round your answer to 3 decimal places.)

This worker is in the lower half of workers but within select the distance from the mean                                                           onethreetwo standard deviation of the mean.

Answer 1

Solution:

Given data:

= 419

Standard deviation = 27

a) It is given that the distribution of the time spent on the job is approximately bell-shaped.Then 68% of the observations will lie within one standard deviation from the mean .

The two times between 68% are computed as follows:

=( 419-27,419+27)

=(392,446)

b) It is given that the distribution of the time spent on the job is approximately bell-shaped.Then 95% of the observations will lie within two standard deviation from the mean .

The two times between 95% are computed as follows:

={419-(2*27),419+(2*27)}

=(365,473)

c) It is given that the distribution of the time spent on the job is approximately bell-shaped.Then 99.7% of the observations will lie within three standard deviation from the mean .

The two times between 99.7% are computed as follows:

={ 419-(3*27),419+(3*27)}

=(338,500)

d) The percentage of time between 358 and 480 is computed as follows:

p(358<X<480) =  

P(-2.259 < Z < 2.259)

= NORM.S.DIST (-2.259,TRUE)-NORM.S.DIST (2.259,TRUE) (use this function in excel ).

= 0.987 - 0.0122

=0.9748.

Thus, 97.48% of the time lie between 358 & 480 minutes if the distribution is unknown.

e) The Z-score for the worker who spent 400 minutes on the job is computed as follows:

Z=(400-419)/27

= -0.70.

The z-score is -0.70.

By rule of thumb any z-value which is below -2 or above 2 is considered as "un-usual " Thus this value is usual.