Suppose that fx ex73 for 73 SolutionTaking the integral of

Suppose that f(x) = e^-(x-7.3) for 7.3

Solution

Taking the integral of f(x),

Integral [f(x)dx] = -exp(-x + 7.3)

a)

Thus,

P(x>7.3) = -exp(-x + 7.3)|(7.3, infinity) = 0 - (-1) = 1 [ANSWER]

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b)

P(7.3<=x<8.7) = -exp(-x + 7.3)|(7.3, 8.7) = -exp(-8.7 + 7.4) - (-exp(-7.3+7.3))

= 0.753 [ANSWER]

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C)

This is no different from part B, as we just include number less than 7.3, which has 0 probability anyway.

P(x < 8.7) = 0.753 [answer]

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d)

P(x > 8.7) = 1 - P(x < 8.7) = 0.247 [answer]

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e)

Here, x should satisfy

-exp(-x + 7.3) + 1 = 0.957

exp(-x + 7.3) = 0.043

Taking the ln of both sides,

-x + 7.3 = -3.147

x = 10.447 [ANSWER]