A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one
Tattoo. Find the approximate probability that more than 17 and less than 26 of the sampled
Students had at least one tattoo.
A)0.2422
B)0.6644
C)0.4222
D)0.1800

Question

Quizplus · Accepted Answer

This problem can be solved using the normal approximation to the binomial distribution. The mean (μ) of the distribution is n*p = 80*0.25 = 20, and the standard deviation (σ) is sqrt(n*p*(1-p)) = sqrt(80*0.25*0.75) ≈ 4.33. To find the probability that more than 17 and less than 26 students have at least one tattoo, we convert these values to z-scores and use the standard normal distribution. The z-score for 17 is (17-20)/4.33 ≈ -0.69, and for 26 is (26-20)/4.33 ≈ 1.39. Looking these up in the z-table or using a calculator, the probability of being between these z-scores is approximately 0.6644, making option B the correct answer.

A Study of College Students Stated That 25% of All