Lesson 5.4 Analyzing Binomial Variables Due 2/2 PM

Mean and Standard Deviation:

Mean:   

SD:        

Required

1

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.

Required

1

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.

Required

1

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.

Required

1

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.

Required

3

How is the mean and standard deviation of Y related to the mean and standard deviation of X?
Explain why this makes sense.

Required

1

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.

Required

3

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.
Interpret the mean from #6:
If many many sets of ________________ were randomly selected the average amount  of ____________________________is ________ .

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.

Required

4

Interpret the standard deviation of X.
The amount of _____________ that_____________________  typically varies from the mean of ________  by about __________ .

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.

Required

2

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.

Required

1

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.

Required

1

#12 continued:
Find the probability that at least 2 of the elk survive to adulthood.

Required

1

When rolling two fair, 6-sided dice, the probability of rolling doubles is 1/6. Suppose Elias rolls the dice 4 times. 
Let W = the number of times he rolls doubles.
Use the following:
statsmedic.com/applets, probability, binomial distribution

Fill in the corresponding blanks:
n = the number randomly selected = 4
p = the probability in decimal form = 0.1667

Use the exact formual to fill in the distribution table below, you will create a Probability Distribution Table for W. Work with a partner.

Find the probability that Elias rolls doubles at most 1 times.
Round to 3 places past the decimal point.

Required

1

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.

Required

1

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.

Lesson 5.4 Analyzing Binomial Variables Due 2/2 PM

How is the mean and standard deviation of Y related to the mean and standard deviation of X? Explain why this makes sense.

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.

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

How is the mean and standard deviation of Y related to the mean and standard deviation of X? Explain why this makes sense.

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.

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

How is the mean and standard deviation of Y related to the mean and standard deviation of X?
Explain why this makes sense.

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.

#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.

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

How is the mean and standard deviation of Y related to the mean and standard deviation of X?
Explain why this makes sense.

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.

#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.

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