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Biblioteka

Lesson 5.4 Analyzing Binomial Variables Due 2/2 PM

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17

Mean and Standard Deviation:

Mean:  

SD:        

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Pitanje 1
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.

Pitanje 2
2.

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.

Pitanje 3
3.

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.

Pitanje 4
4.

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.

Pitanje 5
5.

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

Explain why this makes sense.

Pitanje 6
6.

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.

Pitanje 7
7.
Drugi mogući odgovor:
5.5
times the light was red
10 workdays
Pitanje 8
8.

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.

Pitanje 9
9.
Drugi mogući odgovor:
have a red light
1.573
5.5
workdays

Use statsmedic.com/applets , probability, binomial distributions:

Fill in the corresponding blanks:

n = the number randomly selected

p = the probability in decimal form

Select plot distribution.

Pitanje 10
10.

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.

Pitanje 11
11.

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.

Pitanje 12
12.

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.

Pitanje 13
13.

#12 continued:

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

Pitanje 14
14.

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.

Drugi mogući odgovor:
0 sixes
0.1158
0.0154
4 sixes
3 sixes
0.0008
2 sixes
1 six
0.3858
0.4822
Pitanje 15
15.

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

Round to 3 places past the decimal point.

Pitanje 16
16.

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.

Pitanje 17
17.

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.