Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?
A)Exponential distribution
B)Poisson distribution
C)Normal distribution
D)Uniform distribution

Question

Quizplus · Accepted Answer

Since the sample size is large (10,000) and we are interested in the probability of a binary outcome (preferring Coca-Cola or not), we can use the normal distribution to approximate the binomial distribution. Specifically, we can use the normal approximation to the binomial distribution with a mean of 6000 (0.6 x 10,000) and a standard deviation of approximately 77.46 (sqrt(0.6 x 0.4 x 10,000)). We can then calculate the probability of at least half the sample (5000) preferring Coca-Cola using standard normal distribution tables or a calculator with a normal cumulative distribution function.

Suppose That Past History Shows That 60% of College Students