Question

Determine if the random variable from the experiment follows a Binomial Distribution. A random sample of 150 adults is selected. Each person is asked if they have an American Express card. The number of adults with an American Express card in the sample is recorded. It is known that the percentage of adults with an American Express card is 28%. 1. There there are two mutually exclusive outcomes (success/failure). [ Select ] 2. Since a sample size of 150 is less than 5% of the total population of adults, the trials are independent. [ Select ] 3. There is a fixed number of trials. [ Select ] 4. The probability of success is the same for each trial of the experiment. [ Select ] The random variable follows a Binomial Distribution.

Answer 1

Explanation:

A binomial distribution refers to the probability of a SUCCESS or FAILURE outcome in an experiment that is repeated severally.

A binomial distribution must satisfy some conditions which include:

The number of observations must be fixed, Each observation must be independent., Each observation represents either success of failure i.e. one of the two outcomes and the probability of success, p (and hence failure, q) for each outcome is same.

From the question given; we have the concluded the following answers :

Since the percentage of adults with an American Express card is 28%

Pr (success i.e p) = 0.28.

Then q = 1 - p

q= 1 - 0.28

q = 0.72

1. True. Whether the person has the card or not are mutually exclusive. with p = 0.28 and q = 0.72

2. True. Trials are independent.

3. True. Number of trials are fixed, n = 150

4. True. probability of success will remain same for each trial , p = 0.28

Hence, True, the random variable follows a binomial distribution