Complete Question
The complete question is shown on the first uploaded image
Answer:
a
Yes the selection of 15 is a binomial experiment
b
[tex]P(r = 15) = 3.2768 *10^{-11}[/tex]
c
[tex]P(r = 5) = 0.1032[/tex]
d
[tex]P(r \ge 1 ) = 0.9648 [/tex]
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
[tex]P(r = n) = ^nC_r * p^r * q^{n-r}[/tex]
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
[tex] q = 1 - p [/tex]
=> [tex] q = 1 - 0.20 [/tex]
=> [tex] q = 0.80 [/tex]
So
[tex]P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}[/tex]
[tex]P(r = 15) = 3.2768 *10^{-11}[/tex]
Considering question c
Generally the probability that exactly five of the selected adults save nothing for retirement is mathematically represented as
[tex]P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}[/tex]
[tex]P(r = 5) = 0.1032[/tex]
Considering question d
Generally the probability that at least one of the selected adults saves nothing for retirement is mathematically represented as
[tex]P(r \ge 1 ) = 1 - P (r = 0 )[/tex]
[tex]P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}][/tex]
[tex]P(r \ge 1 ) = 1 - 0.0352[/tex]
[tex]P(r \ge 1 ) = 0.9648 [/tex]
