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, 49% 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 five adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)
Incorrect: Your answer is incorrect.

(b) Out of five adults, all are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)


(c) Out of five adults, exactly three are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

Answer 1

We can use the binomial distribution formula to calculate the probabilities in this scenario. The formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting k successes

n is the total number of trials

p is the probability of success in each trial

(n choose k) is the binomial coefficient, which can be calculated as n! / (k! * (n - k)!)

(a) Out of five adults, none is concerned that employers are monitoring phone calls.

Here, k = 0 (zero successes), n = 5, and p = 0.49 (the probability of success).

Using the binomial distribution formula:

P(X = 0) = (5 choose 0) * 0.49^0 * (1 - 0.49)^(5 - 0) = 0.105

So the probability of none of the five adults being concerned is 0.105, or approximately 0.105.

(b) Out of five adults, all are concerned that employers are monitoring phone calls.

Here, k = 5 (all successes), n = 5, and p = 0.49.

Using the binomial distribution formula:

P(X = 5) = (5 choose 5) * 0.49^5 * (1 - 0.49)^(5 - 5) = 0.013

So the probability of all five adults being concerned is 0.013, or approximately 0.013.

(c) Out of five adults, exactly three are concerned that employers are monitoring phone calls.

Here, k = 3, n = 5, and p = 0.49.

Using the binomial distribution formula:

P(X = 3) = (5 choose 3) * 0.49^3 * (1 - 0.49)^(5 - 3) = 0.270

So the probability of exactly three adults being concerned is 0.270, or approximately 0.270.