Question

The Bureau of Labor Statistics’ American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged 0.35 hour (21 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.1 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends: Less than 18 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.) More than 2 hours. (Round your answers to 4 decimal places.) Between 36 minutes and 108 minutes using a computer for leisure. (Round your answers to 4 decimal places.) Find the 22th percentile. Seventy-eight percent spend more than what amount of time? (Round your answers to 2 decimal places.)

Answer 1

a) for age 75 and over : P(less than 18 minutes) =1-e^{-18/(0.35*60)} =0.5756

for age ages 15 to 19 : P(less than 18 minutes) =1-e^-18/(1.1*60) =0.2387

b)

for age 75 and over : P( More than 2 hours ) =e^{-18/(0.35*60)} =0.0033

for age ages 15 to 19 : P( More than 2 hours ) =e^-18/(1.1*60) =0.1623

c)

for age 75 and over : P( Between 36 minutes and 108 minutes ) =0.1743

for age ages 15 to 19 : P( Between 36 minutes and 108 minutes ) =0.3849

d)

for age 75 and over : 22nd percentile = 5.22 minutes

for age ages 15 to 19 : 22nd percentile = 16.40 minutes