Question

Based on a​ poll, among adults who regret getting​ tattoos, 15 15​% say that they were too young when they got their tattoos. Assume that eight eight 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. nothing ​(Round to four decimal places as​ needed.) b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. nothing ​(Round to four decimal places as​ needed.) c. Find the probability that the number of selected adults saying they were too young is 0 or 1. nothing ​(Round to four decimal places as​ needed.) d. If we randomly select eight eight ​adults, is 1 a significantly low number who say that they were too young to get​ tattoos? ▼ Yes, No, because the probability that ▼ more than 1 at most 1 exactly 1 less than 1 at least 1 of the selected adults say that they were too young is ▼ equal to less than greater than 0.05.

Answer 1

Answer 2

To solve this problem, we can use the binomial probability formula, which is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where: P(X = k) is the probability of getting exactly k successes (in this case, the selected adults saying they were too young). C(n, k) is the number of combinations of n items taken k at a time (also known as the binomial coefficient). p is the probability of success (in this case, the probability that an adult regrets getting a tattoo for being too young). n is the total number of trials (in this case, the number of selected adults).

Given: p = 15% = 0.15 (probability of an adult regretting the tattoo for being too young) n = 8 (total number of selected adults)

Let's calculate the probabilities for parts (a), (b), and (c):

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

P(X = 0) = C(8, 0) * (0.15)^0 * (1 - 0.15)^(8 - 0) P(X = 0) = 1 * 1 * 0.364 * 1 P(X = 0) = 0.364

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

P(X = 1) = C(8, 1) * (0.15)^1 * (1 - 0.15)^(8 - 1) P(X = 1) = 8 * 0.15 * 0.364^7 P(X = 1) ≈ 0.3658

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

P(X = 0 or X = 1) = P(X = 0) + P(X = 1) P(X = 0 or X = 1) = 0.364 + 0.3658 P(X = 0 or X = 1) ≈ 0.7298

d. If we randomly select eight adults, is 1 a significantly low number who say that they were too young to get tattoos?

To determine if 1 is a significantly low number, we need to compare the probability of at most 1 adult saying they were too young (P(X ≤ 1)) to a significance level (usually 0.05 for a 5% level of significance).

P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.364 + 0.3658 ≈ 0.7298

The probability of at most 1 adult saying they were too young is approximately 0.7298, which is greater than 0.05. Therefore, 1 is not a significantly low number, and we fail to reject the null hypothesis that the number of adults saying they were too young is within the expected range.