A study investigated the use of social media by freshman. One question asked if the person answering ever stayed up late to chat with friends and ended up sleep deprived. It was thought that at least 80% of all people of freshman age would stay up late. If the study sampled 400 students, which of the following statements is true? A)The number of students in the sample who stay up late follows a binomial distribution with $\mu$ = 320 and variance $\sigma$²= 64. B)The number of students in the sample who stay up late can be approximated by a Normal distribution with mean $\mu$= 320 and variance $\sigma$²= 64. C)The number of students in the sample who stay up late can be approximated by a Normal distribution with mean $\mu$ = 320 and standard deviation $\sigma$ = 8. D)All of the answer options are correct.

Question

Quizplus · Accepted Answer

The sample size is large (n = 400) and the probability of success (p = 0.8) is not close to 0 or 1, so the binomial distribution can be approximated by a normal distribution. The mean of the normal distribution is np = 400 * 0.8 = 320, and the variance is np(1-p) = 400 * 0.8 * 0.2 = 64. The standard deviation is the square root of the variance, which is 8.

A Study Investigated the Use of Social Media by Freshman μ\muμ

A Study Investigated the Use of Social Media by Freshman $\mu$