1. Self-employed indiviuals in the United States work an average (mean) of 44.5

Question

1. Self-employed indiviuals in the United States work an average (mean) of 44.5 hours per week, with a standard deviation of 14.5 hours. Assume this variable is approximately normally distrubuted to answer the following questions.

a. What is the probability that a randomly chosen self employed individual works more than 48 hours per week?

b. What proportion of self-employed indiviuals work less than 30 hours per week?

c. Determine the 80th percentile of hours worked per week for self-employed individuals. Approximate the nearest tenth and label your answer with proper units.

Explanation / Answer

for normal distirbution ; z score =(X-mean)/std deviaiton

therefore probability that a randomly chosen self employed individual works more than 48 hours per week

=P(X>48)=1-P(X<48)=1-P(Z<(48-44.5)/14.5)=1-P(Z<0.2414)=1-0.5954 =0.4046

b) proportion of self-employed indiviuals work less than 30 hours per week =P(X<30)

=P(Z<(30-44.5)/14.5)=P(Z<-1)=0.1587

c) for 80th percentiel ; z score =0.8416

therefore corresponding hours worked per week for self-employed individuals =mean +z*std deviation

=44.5+0.8416*14.5=56.7 Hours

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