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 1.0 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 16 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 32 minutes and 96 minutes using a computer for leisure. (Round your answers to 4 decimal places.) Find the 35th percentile. Sixty-five percent spend more than what amount of time? (Round your answers to 2 decimal places.)

Answer 1

a) proportion of  age 75 and over  Less than 16 minutes =1-e^-16/21 =0.5332

proportion of  age 15 to 19  : Less than 16 minutes =1-e^-16/60 =0.2341

b)

proportion of  age 75 and over  more than 2 hours =e^-120/21 =0.0033

proportion of  age 15 to 19  : more than 2 hours =e^-120/60 =0.1353

c)

proportion of  age 75 and over  Between 32 minutes and 96 minutes =e^-32/21-e^-96/21 =0.2075

proportion of  age 15 to 19  :  Between 32 minutes and 96 minutes =e^-32-e^-96/60 =0.3847

65th percentile of  age 75 and over =-21*ln(1-0.65)=22.05

65th percentile of  age 15 to 19 =-60*ln(1-0.65)=62.99