Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.Surveying Senators Ten different senators from the 113th Congress are randomly selected without replacement, and the numbers of terms that they have served are recorded.

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Asked Jan 9, 2020
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Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.

Surveying Senators Ten different senators from the 113th Congress are randomly selected without replacement, and the numbers of terms that they have served are recorded.

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Expert Answer

Step 1

Conditions for a binomial distribution:

  • There are a fixed number of trials (n).
  • Each trial must be independent of each other.
  • Each trial has two possible outcomes, success and failure.
  • The probability of success is constant for each trial.
Step 2

From the given procedure,

  1. From the given procedure, there are 10 senators who are randomly selected. Thus, the number of trials (n) is 10. That is, there are a fixed number of trials. Hence, requirement 1 is satisfied.
  2. The selection of senators is done without replacement. Here, 10 senators are more than 5% of the population of 100 sena...

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