[The following information applies to the questions displayed below.] The Bureau

Question

[The following information applies to the questions displayed below.]

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 0.20 hour (12 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 0.8 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends:

rev: 05_18_2015_QC_CS-14973

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 0.20 hour (12 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 0.8 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends:

Explanation / Answer

Solution:

Back-up Theory

If X ~ Exponential with parameter (average inter-event time), the pdf (probability density function) of X is given by f(x) = (1/)e-x/, 0 x < ………………………………(1)

CDF (cumulative distribution function), F(t) = P(X t) = 1- e-t/……………….…(2)

From (2), P(X > t) = e-t/……………….……………………………………………(3)

Now, to work out the solution.

Let X = amount of time spent per day using a computer for leisure by individuals aged 75 and over and

Y = amount of time spent using a computer for leisure by individuals aged 15 to 19.

Then, we are given: X ~ Exp(0.2) ………………………………………………(4) and

Y~ Exp (0.8)………………………………………………………………………(5)

Proportion of each group that spends more than 2 hours in using computer for leisure

= P(X > 2) for the older group and P(Y > 2) for the younger group.

Vide (3) and (4): P(X > 2) = e-(2/0.2) = = e-10 = 4.53999E-05

Vide (3) and (5): P(Y > 2) = e-(2/0.8) = = e-2.5 = 0.082084

So,

Proportion of individuals aged 75 and over that spends more than 2 hours in using computer for leisure = 0.0005 ANSWER 1

Proportion of individuals aged 15 to 19 that spends more than 2 hours in using computer for leisure = 0.0821 ANSWER 2

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