In each of the following situations, is it reasonable to use a binomial distribu

Question

In each of the following situations, is it reasonable to use a binomial distribution for the random variable X? If it is not reasonable to use the binomial distribution, explain why. If it is reasonable to use the binomial distribution, simply give the parameters. If there are not numerical values specified for n and p. describe in words what n and p represent. (a) In a random sample of students in a fitness study, X is the mean daily exercise time of the sample. (b) A manufacturer of running shoes picks a random sample of 20 shoes from the production of shoes each day for a detailed inspection. X is the number of pairs of shoes with a defect. (c) A nutrition study chooses an SRS of college students. They are asked whether or not they usually eat at least five servings of fruits or vegetables per day. X is the number who say that they do. (d) X is the number of days during the school year when you skip a class.

Explanation / Answer

a) no as proportion not given, as well time is a continuous function while binomial distribution is discrete distribution function

b) here we can apply. n=20 ; p is proportion of defective shoes

c)we can apply binomial here, n=sample sizee of SRS

and p=proportion of student who eat at least five servings of fruit or vegetables per day

d) no as number of trails is not fixed..

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