A company has 4 service trucks. Let X represent the number of trucks that are no

Question

A company has 4 service trucks. Let X represent the number of trucks that are not working at any point in time. Consider the probability model shown below for X. What is the probability that exactly 2 of the trucks are not working at any point in time? Give your answer to two decimal places. What is the probability that fewer than 2 of the trucks are not working at any point in time? Give your answer to two decimal places. What is the probability that more than 2 of the trucks are not working at any point in time? Give your answer to two decimal places. What is the expected number of trucks that are not working at any point in time? Give your answer to two decimal places. What is the expected value of X^2? Give your answer to two decimal places. What is the variance of X? Give your answer to four decimal places. What is the standard deviation of X? Give your answer to four decimal places.

Explanation / Answer

a)

P(2) = 0.17 [ANSWER]

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b)

P(x<2) = 0.23 + 0.23= 0.46 [ANSWER]

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c)

P(x>2) = 0.07 + 0.3 = 0.37 [ANSWER]

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d)

Consider:

Thus,  
  
E(x) = Expected value = mean = Sum(xP(x)) =    1.98 [ANSWER]

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e)

E(x^2) = Sum(x^2 P(x)) = 6.34 [ANSWER]

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f)

Var(x) = E(x^2) - E(x)^2 =    2.4196 [ANSWER]

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g)

s(x) = sqrt [Var(x)] =    1.5555 [ANSWER]

x P(x) x P(x) x^2 P(x) 0 0.23 0 0 1 0.23 0.23 0.23 2 0.17 0.34 0.68 3 0.07 0.21 0.63 4 0.3 1.2 4.8

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