Determine whether or not the random variable x is a binomial random variable. if so, give the values of n and p. if not, explain why not. a. x is the number of dots on the top face of fair die that is rolled. b. x is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.

Both are binomials.

Step-by-step explanation:

Given that

a) X is the number of dots on the top face of fair die that is rolled.

When a fair die is rolled, there will be 1 to 6 numbers on each side with dots in that.  Each time a die is rolled the events are independent.  Hence probability of getting a particular number in the die is 1/6. There will be two outcomes either the number or not the number.  Hence X no of times we get a particular number of dots on the top face of fair die that is rolled is binomial with n = no of rolls, and p = 1/6

b) X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.

Here X has two outcomes whether defective or non defective.  EAch part is independent of the other in the sense that the probability for each trial is constant with 0.02% =p and no of trials = n = 10.

(4,5

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