91Ó°ÊÓ

It is given that 20% of people say that they were too young when they got their tattoos.

A sample of 5adults is selected.

Let X denote the number of adults who say they were too young when they got their tattoos.

Let success be defined as getting an adult who says that he/she was too young when they got their tattoos.

The number of trials (n) is given to be equal to 5.

The probability of success is given as follows:

$$\begin{gathered} p=20\% \\ =\frac{20}{100} \\ =0.20 \end{gathered}$$

The probability of failure is given as follows:

$$\begin{gathered} q=1-p \\ =1-0.20 \\ =0.80 \end{gathered}$$

The following binomial probability formula is used:

$P\left(X=x\right)={}^n{C}_x{\left(p\right)}^x{\left(q\right)}^{n-x}$

a.

The number of successes required in 5 trials should be x=0.

Using the binomial probability formula, the probability that none of the adults says that they were too young to get tattoos is computed below:

$$\begin{gathered} P\left(X=0\right)={}^5{C}_0{\left(0.20\right)}^0{\left(0.80\right)}^{5-0} \\ =0.32768 \end{gathered}$$

Therefore, the probability that none of the adults says they were too young to get tattoos is equal to 0.32768.

b.

The number of successes required in 5 trials should be x=1.

Using the binomial probability formula, the probability that exactly 1 adult says that he/she was too young to get tattoos is computed below:

$$\begin{gathered} P\left(X=1\right)={}^5{C}_1{\left(0.20\right)}^1{\left(0.80\right)}^{5-1} \\ =0.4096 \end{gathered}$$

Therefore, the probability that exactly 1 adult says he/she was too young to get tattoos is equal to 0.4096.

c.

The probability that the number of adults saying they were too young is 0 or 1 is computed below:

$$\begin{gathered} P\left(Xâ\copyright ½1\right)=P\left(X=0\right)+P\left(X=1\right) \\ ={}^5{C}_0{\left(0.20\right)}^0{\left(0.80\right)}^{5-0}+{}^5{C}_1{\left(0.20\right)}^1{\left(0.80\right)}^{5-1} \\ =0.73728 \end{gathered}$$

Therefore, the probability that the number of adults saying they were too young is 0 or 1 is equal to 0.73728.

d.

The number of successes (x) of a binomial probability value is said to be significantly low if

$P\left(x\text{or}\text{fewer}\right)â\copyright ½0.05$.

Here, the number of successes (people who believe they were too young to get tattoos) is equal to 1.

$$\begin{gathered} P\left(1\text{or}\text{fewer}\right)=0.73728 \\ >0.05 \end{gathered}$$

Thus, it can be said that out of 5 adults, 1 is not a significantly low number who say that they were too young to get tattoos.