Question

Select all instances in which the variable described is binomial.

a. A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails.
b. A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
c. Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.
d. There are two banking options for customers of ABC Bank, checking or savings. The random variable represents the total number out of 567 customers with a checking account.
e. The probability of drawing an ace in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of ace cards observed.

Answer 1

A & C

Explanation:

Option A: The variable described is binomial because we have a value of n for the experiment and a probability of success 0.5 due to the fact that we have only two possible outcomes, which satisfy the condition of chances of success and failure.

Option B: The variable described is not binomial because the outcome does not fall under the criteria of chances of success or failure of due to the fact that it's possible we have more than two criteria to classify the product.

Option C: The variable described is binomial because we have a definite value of n = 6 with a probability of success = 0.3. Thus, probability of failure will be 0.7 and so it fulfills the condition of success and failure.

Option D: The variable described is not binomial because we don't know if the 2 options are independent of each other.

Option E: Variable describes is not binomial because the cards are drawn without replacement. Also, each time that king is selected, the probability of another king being selected is not the same and for thus the variable is not a a binomial