Question

The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number resulting in a defect. Assume the births are independent. Identify an appropriate probability model for X. a. binomial distribution with n

Answer 1

BINOMIAL DISTRIBUTION

Explanation:

To find out 'x' successes out of 'n' trials, Binomial Distribution is used.

Success = Birth Defect ;

• Prob (success) = Prob (Birth defect) = 1/33 = 0.030
• Prob (no success) = Prob (no birth defect) = 1- 0.030 = 0.97

n = total trials = 5 births (given)

Let 'x' be the no. of successes (defective births) out of 5 ;

P(n, x) = nCx p^x (1 - p)^(n - x)

Eg, with given info :- P (5,x) = 5Cx. (0.030)^x. (0.97)^ (n-x)

Answer 2

The appropriate probability model for X is a Binomial distribution,

X
`\sim` Bin (n = 5, p = 1/33).

Explanation:

The random variable X 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 p = 1/33.

A random sample of n = 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 X 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 (n = 5, p = 1/33).