Suppose that past experience has shown that the likelihood that a personal compu

Question

Suppose that past experience has shown that the likelihood that a personal computer is upgraded within one year of purchase is 0.25. If four personal computers are randomly selected, what is the probability that all four are upgraded? none is upgraded? at least three are upgraded? fewer than two are upgraded? What assumptions are necessary in (a)? What are the mean and standard deviation of the probability distribution in (a)? What would be your answers in (a) if the likelihood that a personal computer is upgraded is 0.15?

Explanation / Answer

There are two outcomes and each is independent.

X = no of computers which get upgraded is binomial with p = 0.25 and n =4

a) 1) 0.00391

2) 0.3164

3) 0.0469

4) 0.7383

b) Each computer is independent

c) E(X) = np = 1

Var(x) = npq = 0.75

std dev = 0.866

d) 0.00051

a >d since p for each success is more in first case

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