statistics

The Information Systems Audit and Control Association surveyed office workers to learn about the anticipated usage of office computers for personal holiday shopping. Assume that the number of hours a worker spends doing holiday shopping on an office computer follows an exponential distribution.

Round your answers to four decimal places.

a.)The study reported that there is a .53 probability that a worker uses the office computer for holiday shopping 5 hours or less. Is the mean time spent using an office computer for holiday shopping closest to 5.5, 6, 6.6, or 7 hours?
The answer is 6.6.

b.)Using the mean time from part (a), what is the probability that a worker uses the office computer for holiday shopping more than 10 hours?

c.) What is the probability that a worker uses the office computer for holiday shopping between four and eight hours?

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  1. If the mean = 6.6, then the probability density function is:
    f(x) = (1/6.6)e^(-x/6.6)

    P(x>10) = 1- int_{0}^{10} ((1/6.6)e^(-x/6.6))dx
    = e^(-10/6.6)
    ~ 0.2198

    P(4<x<8) = P(x>4) - P(x>8)
    = e^(-4/6.6) - e^(-8/6.6)
    ~ 0.2479

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