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

Answer: a. , c. , d., e.

Explanation:

A variable that counts how many times a certain event occurs in a particular number of trials is known as binomial random variable.

For each trial, there exist only two outcomes .

The probability of for each event is the same on each trial.

a. Event has two outcomes with same probability as 0.50, therefore the random variable represents the total number of flips required to get tails is a binomial random variable.

b. Total guidelines are 5.

Here total outcomes are not 2 , it does not meet with the conditions of binomial.

c. The random variable represents the total number of children from this pair of parents with blue eyes has two outcomes (where has or not.)

also, the probability of having blue eyes is same in each trial, so it represents binomial random variable.

d. The random variable represents the total number out of 567 customers with a checking account has two outcomes (checking or savings).

So, it represents binomial random variable.

e. The random variable represents the total number of ace cards observed has two outcomes ( ace or not ace).

So it represents the binomial random variable.