Statistics for a diverse society 7th edition chapter 6 question 10 The number of

Question

Statistics for a diverse society 7th edition chapter 6 question 10 The number of hours people work each week varies widely for many reasons. Using the 2010 GSS, you find that the mean number of hours worked last week was 40.62, with a standard deviation of 15.26 hr, based on a sample size of 838.

a. Assume that hours worked is approximately normally distributed in the sample. What is the probability that someone in the sample will work 60 hr or more in a week? How many people in the sample of 894 should have worked 60 hr or more?

b. What is the probability that someone will work 30 hr or fewer in a week (ie. work part time)? How many people does this represent in the sample?

c. What number of hours worked per week corresponds to the 60th percentile?

Explanation / Answer

mean=40.62

stddev=15.26

sample=838

a)Someone worked 60hrs=(60-40.62)/15.26 =1.27 std dev to the right of mean.

Hence Z(1.27)=0.89786

Hence1-Z=0.10214=10.214% is the prob that someone will work>60hrs

Hence number of people=894*0.10214=91.313 =91 persons

b)30hrs or less=(40.62-30)/15.26 =0.696 std dev to the left of mean

Hence Z(-0.696)=1-Z(0.696)=0.2435=24.35%

Hence number of people=838*0.2435=204 people

c)60% percentile is the number of hour below which there is 60% of the population

Hence Z(x)=0.6 gives x=0.25334

Hence 0.25334 stddev to the right of mean

Gives (t-40.62)/15.26=0.25334 gives t=44.486hrs or 44.5hrs

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