IXL - Mean, variance, and standard deviation of binomial distributions (Precalculus practice)

Jayla is the archery counselor at a summer camp. She has determined that there is a

15%

chance that a camper will hit the target on the first try using a bow and arrow.

If there are 2 campers who are using a bow and arrow, what is the mean of the number of campers who hit the target on the first try?

Write your answer as a decimal.

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question

A waiter believes that if he returns to a customer's table three times during the meal, then there is a

71%

chance the customer will tip well.

Assuming the waiter's belief is correct, if the waiter returns to 2 customers' tables three times, what is the mean of the number of times the waiter is tipped well when he returns to a customer's table three times?

Write your answer as a decimal.

key idea

A binomial experiment consists of identical and independent trials. In each trial there are two outcomes: success and failure.

In a binomial experiment, the number of successes is a random variable. Its probability distribution is called the binomial

distribution.

The binomial distribution depends on

the number of trials, and

the probability of success. Sometimes 1 -

the probability of failure, is written as

If a random variable has a binomial distribution, its mean, variance, and standard deviation are given by:

mean:

𝜇

variance:

𝜎

standard deviation:

𝜎

solution

Interpret the situation as a binomial experiment.

Identify the trials.

A trial is the waiter returning to a customer's table three times during a meal.

Identify a success.

A trial is a success if the customer tips well. It is a failure if the customer does not tip well.

Find the mean.

The question describes a binomial experiment in which the number of trials is 2, the probability of success is 0.71, and the probability of failure is

–

0.71

0.29

Use the formula for the mean of a random variable with a binomial distribution with

0.71

and

0.29

𝜇

0.71

1.42

So, the mean is 1.42.

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