3. Determine whether each of the following random variables has a binomial distr

Question

3. 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 3s in 10 rolls of a fair die with 6 sides 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 X= the same as (b), but half the questions have four choices and the other half have three X-the number of women and 15 men X-the total weight of 15 randomly selected apples c. d. women in a random sample of 8 students from a class with 20 e.

Explanation / Answer

a) X is the Binomial random variable with n=10 and p=1/6.( Probability of getting three in each rolls)

b) X is Binomial random variable with n=40,p=1/4. ( Probability of getting a question correct is 1/4)

c) X is not a Binomial random variable since probability does not remain same for each outcomes.

d) X is a Binomial random variable with n=8,p=20/35

e)X is not the Binomial random variable since the weight of apples is a continuous.

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