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10 August, 23:09

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.

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  1. 10 August, 23:58
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    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.
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