Determine whether each of the following Random Variables has a binomial distribu

Question

Determine whether each of the following Random Variables has a binomial distribution. If it does, identify the values of the parameters n and p (if possible).

(a) X = the number of 4s in10 rolls of a fair die

(b) X = the number of multiple-choice questions a student gets right on a 40-question test, when each question has four choices and the student is completely guessing

(c) X = the same as (b), but half the questions have four choices and the other half have three

(d) X = the number of women in a random sample of 8 students, from a class comprising 20 women and 15 men

(e) X = the total weight of 15 randomly selected apples

(f) X = the number of apples, out of a random sample of 15, that weigh more than 150 g

Explanation / Answer

a) The given random variable has binomial distribution n = 10, p= 1/6

b) The given random variable has binomial distribution n = 40, p= 1/4

c) The given random variable is not having binomial distribution

d) The given random variable has binomial distribution n = 8, p = 20/35 = 4/7

e) The given random variable is not having binomial distribution

f)  The given random variable is not having binomial distribution

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