A candy company claims that 9% of the jelly beans in its spring mix are pink.Suppose that the candies are packaged at random in small bags containing about 50 jelly beans.A class of students opens several bags,counts the various colors of jelly beans,and calculates the proportion that are pink.Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans?

A) A Normal model is appropriate because the 50 bags of jelly beans can be thought of as a random sample of bags and are fewer than 10% of the population of all bags.The success/failure condition is also satisfied because n = 50 ≥ 10.
B) A Normal model is appropriate because the samples are random and independent.Also,the sample size,50,is less than 10% of the population.
C) A Normal model is not appropriate because the sample size is not large enough to satisfy the success/failure condition.For this sample size,np = 4.5 < 10.
D) A Normal model is not appropriate because the sample size,50,is larger than 10% of the population of all bags of jelly beans.
E) A Normal model is not appropriate because the population distribution is not Normal.

Question

Jaquelynn Davis · Accepted Answer

Final Answer : C, Explanation :  The success/failure condition for using a Normal model requires that both np and n(1-p) are greater than or equal to 10. Here, np = 50 * 0.09 = 4.5, which is less than 10, thus not satisfying the condition.

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