Question

Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 38% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following. (a) Out of six adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

Answer 1

a) 0.0568

Explanation:

Let's define the random variable X.

X : ''Number of adults concerned that employers are monitoring phone calls''

X ~ Bi (n,p)

Where n is the sample size and p is the success probability.

n is equal to 6 in this exercise and p = 0.38

We are going to call ''a success'' to an adult concerned that employers are monitoring phone calls.

The probability function for X is

`P(X=x)=(nCx)p^(x)(1-p)^(n-x)`

Where nCx is the combinatorial number define as

`nCx=(n!)/(x!(n-x)!)`

For a) we are looking for
`P(X=0)`

`P(X=0)=(6C0)(0.38)^(0)(1-0.38)^(6-0)=0.62^(6)=0.0568`

There is a probability of 0.0568 that out of six adults, none is concerned that employers are monitoring phone calls.