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Answer:
The appropriate probability model for X is a Binomial distribution,
X Bin (<em>n</em> = 5, <em>p</em> = 1/33).
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of American births resulting in a defect.
The proportion of American births that result in a birth defect is approximately <em>p</em> = 1/33.
A random sample of <em>n</em> = 5 American births are selected.
It is assumed that the births are independent, i.e. a birth can be defective or not is independent of the other births.
In this experiment the success is defined as a defective birth.
The random variable <em>X</em> satisfies all criteria of a Binomial distribution.
The criteria are:
- Number of observations is constant
- Independent trials
- Each trial has only two outcomes: Success and Failure
- Same probability of success for each trial
Thus, the appropriate probability model for X is a Binomial distribution, Bin (<em>n</em> = 5, <em>p</em> = 1/33).