Question

Based on a​ poll, among adults who regret getting​ tattoos, 23​% say that they were too young when they got their tattoos. Assume that nine adults who regret getting tattoos are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.(a) Find the probability that none of the selected adults say that they were too young to get tattoos.(b) Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.(c) Find the probability that the number of selected adults saying they were too young is 0 or 1.(d) It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?

Answer 1

Answer:

a) There is a 9.52% probability that none of the selected adults say that they were too young to get tattoos.

b) There is a 25.28% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) There is a 35.1% probability that the number of selected adults saying they were too young is 0 or 1.

d) 1 is not a significantly low number who say that they were too young to get tattoos.

Step-by-step explanation:

For each adult questioned, there are only two answers possible, two outcomes. Either they were too young when they got their tattoos, or they were not. So this means that we can solve this problem as binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem, we have that:

Nine adults are sampled, so $n = 9$.

23​% say that they were too young when they got their tattoos, so $p = 0.23$.

(a) Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0)

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{9,0}.(0.23)^{0}.(0.77)^{9} = 0.0952$

There is a 9.52% probability that none of the selected adults say that they were too young to get tattoos.

(b) Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1)

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{9,1}.(0.23)^{1}.(0.77)^{8} = 0.2558$

There is a 25.28% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

(c) Find the probability that the number of selected adults saying they were too young is 0 or 1.

$P = P(X = 0) + P(X = 1) = 0.0952 + 0.2558 = 0.351$

There is a 35.1% probability that the number of selected adults saying they were too young is 0 or 1.

(d) It we randomly select 9 adults. Is 1 a significantly low number who say that they were too young to set tattoos?

We say that a value x is significantly low if:

$P(X \leq x) \leq 0.05$

For 1, we have

$P(X \leq 1) =  P(X = 0) + P(X = 1) = 0.0952 + 0.2558 = 0.351$.

A 35.1% probability is greater than a 5% probability, so 1 is not a significantly low number who say that they were too young to get tattoos.

Answer 2

Answer:

Step-by-step explanation:

a) There is a 9.52% probability that none of the selected adults say that they were too young to get tattoos.

b) There is a 25.28% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) There is a 35.1% probability that the number of selected adults saying they were too young is 0 or 1.

d) 1 is not a significantly low number who say that they were too young to get tattoos.

Step-by-step explanation:

For each adult questioned, there are only two answers possible, two outcomes. Either they were too young when they got their tattoos, or they were not. So this means that we can solve this problem as binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which  is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And  is the probability of X happening.

In this problem, we have that:

Nine adults are sampled, so .

23​% say that they were too young when they got their tattoos, so .

(a) Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0)

There is a 9.52% probability that none of the selected adults say that they were too young to get tattoos.

(b) Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1)

There is a 25.28% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

(c) Find the probability that the number of selected adults saying they were too young is 0 or 1.

There is a 35.1% probability that the number of selected adults saying they were too young is 0 or 1.

(d) It we randomly select 9 adults. Is 1 a significantly low number who say that they were too young to set tattoos?

We say that a value x is significantly low if:

For 1, we have

A 35.1% probability is greater than a 5% probability, so 1 is not a significantly low number who say that they were too young to get tattoos.