Lesson 5.4 Analyzing Binomial Variables Due 2/2 PM

When a polling company calls a telephone number at random, there is only a 9% chance that the call reaches a live person and the survey is successfully completed. Suppose the random digit dialing machine makes 15 calls.

Let X = the number of calls that result in a completed survey.

Find the mean of X.

Round to 2 places past the decimal.

When a polling company calls a telephone number at random, there is only a 9% chance that the call reaches a live person and the survey is successfully completed. Suppose the random digit dialing machine makes 15 calls.

Let X = the number of calls that result in a completed survey.

Find the standard deviation of X.

Round to 3 places past the decimal.

When a polling company calls a telephone number at random, there is only a 9% chance that the call reaches a live person and the survey is successfully completed. Suppose the random digit dialing machine makes 15 calls.

Let Y = the number of calls that don’t result in a completed survey.

Find the mean of Y.

Round to 2 places past the decimal.

When a polling company calls a telephone number at random, there is only a 9% chance that the call reaches a live person and the survey is successfully completed. Suppose the random digit dialing machine makes 15 calls.

Let Y = the number of calls that don’t result in a completed survey.

Find the standard deviation of Y.

Round to 3 places past the decimal.

How is the mean and standard deviation of Y related to the mean and standard deviation of X?

Explain why this makes sense.

Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red when he arrives at the intersection on a randomly selected workday.

Suppose we choose 10 of Pedro’s workdays at random and let X = the number of times that the light is red.

Calculate the mean of X, keep all decimal places.

Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red when he arrives at the intersection on a randomly selected workday.

Suppose we choose 10 of Pedro’s workdays at random and let X = the number of times that the light is red.

Calculate the standard deviation of X, round to three places past the decimal.

According to the local traffic department, there is a 55% chance that the light will be red at the intersection.

If the light is red on 7 of the 10 days, do we have convincing evidence that the traffic department’s claim is false?

First:

Compute P(X ≥ 7).

Hint: think about what you will select in statsmedic: exactly, less than, at most, at least, or more than?

Round to three places past the decimal.

This is a numerical answer.

Next:

If the light is red on 7 of the 10 days, do we have convincing evidence that the traffic department’s claim is false?

Use the result above to support your answer.

Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor.

Let X = the number who survive to adulthood.

The probability distribution of X is shown below.

Find the probability that fewer than 3 of the elk survive to adulthood.

#12 continued:

Find the probability that at least 2 of the elk survive to adulthood.

Find the probability that Elias rolls doubles at most 1 times.

Round to 3 places past the decimal point.

About 20% of cars sold in North America are white.

The probability distribution of X = the number of white cars among 6 randomly selected cars is a binomial.

Use statsmedic.com/applets, probability, binomial distribution, to determine the following value.

Find the probability that at least 4 cars in randomly selected groups of 6 cars are white.

About 20% of cars sold in North America are white. The probability distribution of X = the number of white cars among 6 randomly selected cars is a binomial.

Find the probability that at least 4 cars in randomly selected groups of 6 cars are white.