The Bureau of Labor Statistics’ American Time Use Survey showed that the amount

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 0.30 hour (18 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

a.

Less than 14 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.)

  Proportion

   Age 75 and over

   Ages 15 to 19

b.

More than two hours. (Round your answers to 4 decimal places.)

  Proportion

   Age 75 and over

   Ages 15 to 19

Between 28 minutes and 84 minutes using a computer for leisure. (Round your answers to 4 decimal places.)

  Proportion

   Age 75 and over

   Ages 15 to 19

d.

Find the 28th percentile. seventy two percent spend more than what amount of time? (Round your answers to 2 decimal places.)

  Amount of time for individuals ages 75 and over

minutes

  Amount of time for individuals ages 15 to 19

minutes

a.

Less than 14 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.)

Explanation / Answer

Ans:

Cumululative distribution functio for 75 and over:

P(X<=x)=1-e-x/18

Cumululative distribution functio for 15-19:

P(X<=x)=1-e-x/60

a)

For 75 and over:

P(X<=14)=1-e-14/18=1-e-0.778=0.5406

For 15-19:

P(X<=14)=1-e-14/60=1-e-0.233=0.2081

b)2 hrs=120 min

For 75 and over:

P(X>120)=e-120/18=0.0013

For 15-19:

P(X>120)=e-120/60=e-2=0.1353

c)

For 75 and over:

P(28<=X<=84)=e-28/18-e-84/18=0.2111-0.0094=0.2017

For 15-19:

P(28<=X<=84)=e-28/60-e-84/60=0.6271-0.2466=0.3805

d)

For 75 or over:

P(X<=x)=0.28

or

P(X>=x)=0.72=e-x/18

x/18=0.3285

x=5.91 min

For 15-19:

x/60=0.3285

x=19.71 min

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