TABLE 7-4
According to a survey,only 15% of customers who visited the website of a major retail store made a purchase.Random sample sizes of 50 are selected.
-True or False: Referring to Table 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:
- The sample size is large enough (np≥10 and n(1−p)≥10)
- The data are independent
In this case, the sample size is 50, and 15% of customers making a purchase means that p=0.15 and q=0.85. Checking these values, we get np=7.5 and nq=42.5, both of which are greater than 10. Therefore, both requirements are fulfilled and it is appropriate to use a normal distribution to approximate the binomial distribution.

TABLE 7-4 According to a Survey,only 15% of Customers Who Visited the Visited