Question

According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adults in the United States are selected randomly. a. Is the selection of the adults a binomial experiment? Explain. The selection - Select your answer - a binomial experiment because the adults are selected - Select your answer - , - Select your answer - from trial to trial, the trials - Select your answer - independent, and there are - Select your answer - outcomes possible. b. What is the probability that all of the selected adults save nothing for retirement (to 4 decimals)? c. What is the probability that exactly five of the selected adults save nothing for retirement (to 4 decimals)? d. What is the probability that at least one of the selected adults saves nothing for retirement (to 4 decimals)?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 Yes the selection of 15 is a binomial  experiment

b

   $P(r = 15) = 3.2768 *10^{-11}$

c

  $P(r = 5) = 0.1032$

d

$P(r \ge 1 ) = 0.9648$

Step-by-step explanation:

considering question a

Generally for and experiment to be binomial

The trial must be independent

There must be only two outcomes for each trial

Generally given that that the 15 adults are selected randomly which mean that the trials will be independent and that desired outcome is ''ether the adult save something for retirement or the adult saves nothing for retirement ''

Then we can say that the selection of 15 adult at is a binomial experiment

Considering question b

Generally the probability that all of the adults save nothing for retirement is mathematically represented as

$P(r = n) = ^nC_r * p^r * q^{n-r}$

Here C stands for combination

r = 15 i.e all the selected adults

      n is the sample size with value  15

From the question p = 0.20

and q is calculated as

$q = 1 - p$

=> $q = 1 - 0.20$

=> $q = 0.80$

So

$P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}$

$P(r = 15) = 3.2768 *10^{-11}$

Considering question c

Generally the probability that exactly five of the selected adults save nothing for retirement is mathematically represented as

$P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}$

$P(r = 5) = 0.1032$

Considering question d

Generally the probability that at least one of the selected adults saves nothing for retirement is mathematically represented as

$P(r \ge 1 ) = 1 - P (r = 0 )$

$P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]$

$P(r \ge 1 ) = 1 - 0.0352$

$P(r \ge 1 ) = 0.9648$