Question

Based on a poll of 800 adults, 25% of them regret getting their tattoos. Find the mean and standard deviation for the number of people who regret getting their tattoos.

Answer 1

Mean = 200

Standard deviation = 12.25

Step-by-step explanation:

We are given that based on a poll of 800 adults, 25% of them regret getting their tattoos.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 800 adults

            r = number of success

           p = probability of success which in our question is % of adults

                  who regret getting their tattoos, i.e; 25%

LET X = Number of people who regret getting their tattoos

So, X ~ Binom(n = 800, p = 0.25)

Now, Mean of the binomial distribution is given by the following formula;

         Mean, E(X) =  $n \times p$

                            =  $800 \times 0.25$ = 200

Also, the Standard deviation of the binomial distribution is given by the following formula;

        Standard deviation, S.D.(X) =  $\sqrt{n\times p \times (1-p)}$

                                                      =  $\sqrt{800 \times 0.25 \times (1-0.25)}$

                                                      =  $\sqrt{800 \times 0.25 \times 0.75}$

                                                       =  $\sqrt{150}$  =  12.25

Therefore, the mean and standard deviation for the number of people who regret getting their tattoos is 200 and 12.25 respectively.