Explain why not a binomial random variable. wo balls are randomly selected with replacement from a jar that con xplain why x is or is not a binomial random variable. O The random variable x is a binomial random variable since the b O The random variable x is a binomial random variable since there The random variable x is not a binomial random variable since t O The random variable x is not a binomial random variable since t f the experiment is binomial, give the values of n and p. (If the expe 11 compa 11

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**Explanation of Binomial Random Variables:**

**Question:**
Explain why \( x \) is or is not a binomial random variable. (HINT: Compare the characteristics of this experiment with those of a binomial experiment given in this section.)

**Scenario:**
Two balls are randomly selected *with* replacement from a jar that contains seven red and three white balls. The number \( x \) of red balls is recorded.

**Options to Explain:**

- O The random variable \( x \) is a binomial random variable since the balls are selected with replacement. For this reason, the probability \( p \) of choosing a red ball does not change from trial to trial.

- O The random variable \( x \) is a binomial random variable since there is an unequal number of red and white balls in the jar. For this reason, the probability \( p \) of choosing a red ball does not change from trial to trial.

- O The random variable \( x \) is not a binomial random variable since the balls are selected with replacement. For this reason, the probability \( p \) of choosing a red ball changes from trial to trial.

- O The random variable \( x \) is not a binomial random variable since there is an unequal number of red and white balls in the jar. For this reason, the probability \( p \) of choosing a red ball changes from trial to trial.

**Further Instructions:**
If the experiment is binomial, give the values of \( n \) and \( p \). (If the experiment is not binomial, enter NONE.)

- \( n = \) [ ]
- \( p = \) [ ]
Transcribed Image Text:**Explanation of Binomial Random Variables:** **Question:** Explain why \( x \) is or is not a binomial random variable. (HINT: Compare the characteristics of this experiment with those of a binomial experiment given in this section.) **Scenario:** Two balls are randomly selected *with* replacement from a jar that contains seven red and three white balls. The number \( x \) of red balls is recorded. **Options to Explain:** - O The random variable \( x \) is a binomial random variable since the balls are selected with replacement. For this reason, the probability \( p \) of choosing a red ball does not change from trial to trial. - O The random variable \( x \) is a binomial random variable since there is an unequal number of red and white balls in the jar. For this reason, the probability \( p \) of choosing a red ball does not change from trial to trial. - O The random variable \( x \) is not a binomial random variable since the balls are selected with replacement. For this reason, the probability \( p \) of choosing a red ball changes from trial to trial. - O The random variable \( x \) is not a binomial random variable since there is an unequal number of red and white balls in the jar. For this reason, the probability \( p \) of choosing a red ball changes from trial to trial. **Further Instructions:** If the experiment is binomial, give the values of \( n \) and \( p \). (If the experiment is not binomial, enter NONE.) - \( n = \) [ ] - \( p = \) [ ]
Expert Solution
Introduction

When one of the following circumstances holds true, the behavior of count variable is described by the binomial distribution:

  1. Number of observation is fixed 
  2. Each observation must independent 
  3. Each observation must represent one of two outcomes.

 

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