Mathematics: According to a survey of business executives, 78% received a pay raise when they asked for one. A random sample of four executives was selected. The probability that all four received a raised when they asked for one is . 0.056 0.127 0.237 0.370

According to a survey of business executives, 78%

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29.01.2022

The probability that all four received a raised when they asked for one is 0.370.

Step-by-step explanation:

Let the random variable X represent the number of business executives who received a pay raise when they asked for one.

The probability that a business executives received a pay raise when they asked for one is, p = 0.78.

A random sample of n = 4 executives was selected.

The events of any executive receiving a pay raise when they asked for one is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 4 and p = 0.78.

The probability mass function of X is:

$P(X=x)={4\choose x}\ (0.78)^{x}\ (1-0.78)^{4-x};\ x=0,1,2,3...$

Compute the probability that all four received a raised when they asked for one as follows:

$P(X=4)={4\choose 4}\ (0.78)^{4}\ (1-0.78)^{4-4}$

$=1\times 0.37015056\times 1\\\\=0.37015056\\\\\apporx 0.370$

Thus, the probability that all four received a raised when they asked for one is 0.370.

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