According to an article by B.E. Sullivan in Transportation Research (18A, no. 2,

Question

According to an article by B.E. Sullivan in Transportation Research (18A, no. 2, 1984, p. 119), 55% of U.S. corporations say that one of the most important factors in locating a corporate headquarters is the "quality of life" for the employees. If five firms are contacted by the governor of Florida concerning possible relocation to that state, find the probability that at least three say the "quality of life" is an important factor in their decision. What assumptions have you made in arriving at this answer?

Explanation / Answer

In the given question it is specified that 55% of the U.S corporations say that one of the most important factors in locating a corporate headquarters is the “Quality of life” for the employees.

Here, we can assume a binomial distribution,

So, let X be a random variable which denotes the number of firms who say that the quality of life for the employees is important

The probability distribution of a binomial variate is given by

P(X=x)=nCxpx(1-p)n-x

Since, five firms are contacted by the governor of Florida so we have n=5

The theoretical value of the proportion is given as p=55%=0.55

Now, we have to find the probability that at least three firms say that the “quality of life” is an important factor

P(At least three firms say that the quality of life is important) = P(X3) = P(X=3)+P(X=4)+P(X=5)

P(X=3) = 5C3(0.55)3(0.45)2 = 0.33691

P(X=4) = 5C4(0.55)4(0.45)1 = 0.205889

P(X=5) = 5C5(0.55)5(0.45)0 = 0.050328

So, P(X3) = 0.33691+0.205889+0.050328 =0.5931

P(X3) = 0.5931

The assumptions that we make here are

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