QuestionPractice: Probability and Distributions
1. Determine whether the following procedure results in a binomial distribution or a distribution that can be treated as binomial. If it is not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
a. In a Pew Research Center survey of 50 subjects, the ages of the respondents are recorded.
b. A basketball player who makes of his free throws is asked to shoot free throws until he misses. The number of free throws attempted is recorded.
Studdy Solution
STEP 1
1. A binomial distribution requires a fixed number of trials, each with two possible outcomes (success or failure), independent trials, and a constant probability of success.
2. For a distribution to be treated as binomial, it must satisfy the same conditions as a true binomial distribution.
STEP 2
1. Analyze the procedure in part (a) to determine if it results in a binomial distribution.
2. Analyze the procedure in part (b) to determine if it results in a binomial distribution.
STEP 3
Examine the procedure in part (a):
- The procedure involves recording the ages of 50 subjects.
- Determine if the conditions for a binomial distribution are met:
- Fixed number of trials: Yes, there are 50 subjects.
- Two possible outcomes: No, ages are not binary outcomes.
- Independent trials: Yes, assuming each subject's age is independent.
- Constant probability of success: Not applicable, as ages are not binary.
Conclusion: The procedure does not result in a binomial distribution because the outcome is not binary.
STEP 4
Examine the procedure in part (b):
- The procedure involves a basketball player shooting free throws until he misses.
- Determine if the conditions for a binomial distribution are met:
- Fixed number of trials: No, the number of trials is not fixed; it depends on when the first miss occurs.
- Two possible outcomes: Yes, each shot can be a success (made) or failure (missed).
- Independent trials: Yes, assuming each shot is independent.
- Constant probability of success: Yes, the probability of making a shot is .
Conclusion: The procedure does not result in a binomial distribution because there is no fixed number of trials.
The procedure in part (a) does not result in a binomial distribution because the outcome is not binary. The procedure in part (b) does not result in a binomial distribution because there is no fixed number of trials.
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