SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected.
-Referring to Scenario 7-4, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

Question

Quizplus · Accepted Answer

The requirements for using a normal distribution to approximate a binomial distribution are as follows: 
1. The sample size is large enough (n≥10)
2. The population is at least 10 times larger than the sample size (N≥10n)
Since the sample size (50) is large enough and the population size is assumed to be much larger than the sample size, both requirements are fulfilled. Therefore, we can use a normal distribution to approximate a binomial distribution in this scenario. The requirements for using a normal distribution to approximate a binomial distribution are fulfilled when np and n(1-p) are both greater than or equal to 10, where n is the sample size and p is the probability of success. In this scenario, n=50 and p=0.15, so np=7.5 and n(1-p)=42.5, which are both greater than or equal to 10. Therefore, the requirements are fulfilled and a normal distribution can be used to approximate the binomial distribution.

SCENARIO 7-4 According to a Survey, Only 15% of Customers