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Author Question: If this experiment is completed without replacement, explain why x is not a binomial random ... (Read 26 times)

azncindy619

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on: Jul 24, 2018
If this experiment is completed without replacement, explain why x is not a binomial random variable.

Question 2

A carton containing 75 towels is inspected. Each towel is rated first quality or irregular. After all 100 towels are inspected, the number of irregulars is reported as a random variable. Explain why x is a binomial variable


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Expo

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Reply #1 on: Jul 24, 2018
Answer to Question 1

x is not a binomial random variable because the trials are not independent. The
probability of success (get an ace) changes from trial to trial. On the first trial it is 4/52.
The probability of an ace on the second trial depends on the outcome of the first trial; it is
4/51 if an ace is not selected, and it is 3/51 if an ace was selected. The probability of an
ace on any given trial continues to change when the experiment is completed without
replacement.

Answer to Question 2

x is a binomial variable since it satisfies the following properties:
n = 75 repeated identical independent trials (towels), there are only two outcome (first
quality, irregular), p =P(success) = P(irregular), x = number of irregular towels that may
take on any integer value from 0 to 75.


azncindy619

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Reply #2 on: Jul 24, 2018
Both answers were spot on, thank you once again


Expo

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Reply #3 on: Jul 24, 2018
Great! Please up vote :D


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