1.The number of times that a hiker walks over 8 miles each day is what type of data random variable?

1. Discrete
2. Continuous

Question 2Select one answer.10 points

Which of the following is a characteristic of a discrete random variable?

1. It is something you count.
2. It is something you measure.
3. It is something you both measure and count.

Question 3Select one answer.10 points

Which of the following is a discrete data random variable?

1. A person's weight on each year
2. A person's height each birthday
3. Cars finished in a factory each day
4. The volume of water in a swimming pool each day

Question 4Select one answer.10 points

The following three histograms represent the probability distributions of the three random variables X, Y, and Z.

Which of the three random variables has the smallest standard deviation?

1. X
2. Y
3. Z
4. All three random variables have the same standard deviation.

Question 5Select one answer.10 points

The random variable X, representing the number of items sold in a week, has the following probability distribution:

x	0	1	2	3	4	5	6
P(X = x)	0.10	0.20	0.40	0.15	0.05	0.05	0.05

On average, how many items are sold in a week?

1. 6.3
2. 3.0
3. 2.2
4. 2.0
5. 0.1428

Question 6Select one answer.10 points

According the the Pew Research Center, the probability of a randomly selected person living the United States identifying with a particular religious affiliationProtestant Christian; Catholic Christian, Other Christian, Non-Christian (including Jewish, Muslim, Buddhist, Hindu and other religions); and Unaffiliated (the so-called "nones")is shown in the following chart.

Affiliation	Protestant Christian	Catholic Christian	Other Christian	Non-Christian	Unaffiliated "none"
Probability	0.466	0.208	0.033	0.06	0.233

Adapted from "America's Changing Religious Landscape," Pew Research Center, May 12, 2015,http://www.pewforum.org/religious-landscape-study/state/california/

Assuming this data is accurate and stable, what is the probability that a randomly selected Christian living in the United States would identify as Catholic?

1. 0.659
2. 0.707
3. 0.208
4. 0.294

Question 7Select one answer.10 points

The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:

x	0	1	2	3	4	5
P(X = x)	0.20	0.30	0.20	0.15	0.10	0.05

What is the probability that in a given week there will be at most 3 accidents?

1. 0.70
2. 0.85
3. 0.35
4. 0.15
5. 1.00

Question 8Select one answer.10 points

The following three histograms represent the probability distributions of the three random variables X, Y, and Z.

Which of the three random variables has the largest standard deviation?

1. X
2. Y
3. Z
4. All three random variables have the same standard deviation.

Question 1Select one answer.10 points

The probability distribution for the number of defects during an eight hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below.

x	0	1	2	3	4	5
P(X = x)	0.50	0.25	0.15	0.06	0.03	0.01

On average, how many defects are found during an 8-hour shift?

1. 5.3
2. 2.5
3. 0.9
4. 0.50
5. 0.1667

Question 2Select one answer.10 points

Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why.

X	3	6	9	12	15
P(X=x)	4/9	2/9	1/9	1/9	1/9

1. Yes, the values of X are all positive.
2. No, the probabilities do not add up to 1.
3. Yes, the probabilities associated with each X are all positive and they all add up to 1.
4. No, the values of X do not start at 1 and the probabilities do not add up to 1.

Question 3Select one answer.10 points

Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why.

X	20	30	40	50
P(X=x)	1.1	0.6	.2	.1

1. Yes, the probabilities are all positive.
2. No, the values of X are too far apart and the probabilities add up to a value greater than 1.
3. Yes, the probabilities add to 1 and they are all positive.
4. No, while the probabilities are all positive, the P(X=20)=1.1. Probabilities cannot exceed 1.

Question 4Type numbers in the boxes.Part 1:2 pointsPart 2:2 pointsPart 3:2 pointsPart 4:2 pointsPart 5:2 points10 points

Below is a distribution for number of visits to dentists in one year.

X	1	2	3	4	5
P(X=x)	0.26	0.41	0.20	0.06	0.07

Calculate the following probabilities:

a. P(X < 2) =

b. P(X3) =

c. P(1< X3) =

d. P(3X < 5) =

e. P(3 < X < 5) =

Question 5Type numbers in the boxes.Part 1:2 pointsPart 2:2 pointsPart 3:2 pointsPart 4:2 pointsPart 5:2 pointsPart 6:2 points12 points

Below is a probability distribution for the number of failures in an elementary statistics course.

X	0	1	2	3	4
P(X=x)	0.40	0.15	?	0.08	0.13

Determine the following probabilities:

a. P(X = 2) =

b. P(X < 2) =

c. P(X2) =

d. P(X > 2) =

e. P(X = 1 or X = 4) =

f. P(1X4) =

Question 6Type numbers in the boxes.Part 1:5 pointsPart 2:5 points10 points

From past experience, a company has found that in carton of transistors:

92% contain no defective transistors

3% contain one defective transistor,

3% contain two defective transistors, and

2% contain three defective transistors.

Calculate the mean and variance for the defective transistors.

Mean =

Variance =

(Please round answers to 4 decimal places.)

Question 7Select one answer.10 points

First, find the value of the constant,kso that the following table represents a probability distribution for the random variable,xand then findP(x<2).

x	0	1	2	3
P(x)	2k	3k	13k	2k

The probability that P(X < 2) is equal to

1. 0.65
2. 0.15
3. 0.90
4. 0.25
5. 1.00

Question 1Select all that apply.10 points

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:

X: the number of US residents (out of 50) with blood type AB.

Y: the number of Australians (out of 40) with blood type AB.

Z: the total number of individuals (out of 90) with blood type AB.

Which of the following is true about the random variablesX,Y, andZ? Check all that apply.

1. X is a binomial random variable with n = 50 and p = 0.04
2. Y is a binomial random variable with n = 40 and p = 0.015
3. Z is a binomial random variable with n = 90 and p = 0.055

Question 2Select one answer.10 points

In the following random experiment, decide whether the random variable X is binomial or not:

Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent.

1. Binomial
2. Not binomial

Question 3Select one answer.10 points

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:

X: the number of U.S. residents with blood type AB

Y: the number of Australians with blood type AB

What is the probability that exactly 2 of the U.S. residents have blood type AB? (Note: Some answers are rounded)

1. 0.2762
2. 0.04
3. 0.1334
4. 0.0988
5. 0.2646

Question 4Type numbers in the boxes.Part 1:10 pointsPart 2:10 points20 points

According to the CDC, the rate of Cesarean births in the United States in 2013 was about 33%. Suppose a random sample of 200 births is selected. Let X be the number of Cesarean births out of all 200 births. What are the values of the parameters for the binomial random variable X?

n =

p =

Question 5Select all that apply.10 points

Which of the following scenarios are Binomial?

1. A couple decided to continue having children until their first girl is born: X is the total number of children the couple has.
2. A quality control inspector takes a random sample of 20 items from a large lot, inspects each item, classifies it as poor, satisfactory, or good, and counts the number of each type of item in the sample.
3. You observe the sex of the next 20 children born at a local hospital: X is the number of girls among them.
4. An engineer chooses a SRS of 10 switches from a shipment of 10,000 switches. Suppose 10% of the switches in the shipment are bad. The engineer counts the number X of bad switches in the sample.

Question 6Type numbers in the boxes.Part 1:4 pointsPart 2:4 pointsPart 3:4 points12 points

A certain medical test is known to detect 62% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that:

All 10 have the disease, rounded to four decimal places?

At least 8 have the disease, rounded to four decimal places?

At most 4 have the disease, rounded to four decimal places?

Question 7Type numbers in the boxes.Part 1:4 pointsPart 2:4 pointsPart 3:4 points12 points

According to government data, 52% of employed women have never been married. Rounding to 4 decimal places, if 15 employed women are randomly selected:

a. What is the probability that exactly 2 of them have never been married?

b. That at most 2 of them have never been married?

c. That at least 13 of themhave beenmarried?

Question 8Type numbers in the boxes.Part 1:4 pointsPart 2:4 pointsPart 3:4 pointsPart 4:4 pointsPart 5:4 pointsPart 6:4 points24 points

Assume that 12% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:

a. There are some lefties (1) among the 5 people.

b. There are exactly 3 lefties in the group.

c. There are at least 4 lefties in the group.

d. There are no more than 2 lefties in the group.

e. How many lefties do you expect?

f. With what standard deviation?

Question 9Select one answer.10 points

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

1. 0.2013
2. 0.2634
3. 1
4. 0.3020
5. 0.5

The number of times that a hiker walks over 8 miles each day is what type of data random variable?

1. Discrete
2. Continuous

Question 2Select one answer.10 points

Which of the following is a characteristic of a discrete random variable?

1. It is something you count.
2. It is something you measure.
3. It is something you both measure and count.

Question 3Select one answer.10 points

Which of the following is a discrete data random variable?

1. A person's weight on each year
2. A person's height each birthday
3. Cars finished in a factory each day
4. The volume of water in a swimming pool each day

Question 4Select one answer.10 points

The following three histograms represent the probability distributions of the three random variables X, Y, and Z.

Which of the three random variables has the smallest standard deviation?

1. X
2. Y
3. Z
4. All three random variables have the same standard deviation.

Question 5Select one answer.10 points

The random variable X, representing the number of items sold in a week, has the following probability distribution:

x	0	1	2	3	4	5	6
P(X = x)	0.10	0.20	0.40	0.15	0.05	0.05	0.05

On average, how many items are sold in a week?

1. 6.3
2. 3.0
3. 2.2
4. 2.0
5. 0.1428

Question 6Select one answer.10 points

According the the Pew Research Center, the probability of a randomly selected person living the United States identifying with a particular religious affiliationProtestant Christian; Catholic Christian, Other Christian, Non-Christian (including Jewish, Muslim, Buddhist, Hindu and other religions); and Unaffiliated (the so-called "nones")is shown in the following chart.

Affiliation	Protestant Christian	Catholic Christian	Other Christian	Non-Christian	Unaffiliated "none"
Probability	0.466	0.208	0.033	0.06	0.233

Adapted from "America's Changing Religious Landscape," Pew Research Center, May 12, 2015,http://www.pewforum.org/religious-landscape-study/state/california/

Assuming this data is accurate and stable, what is the probability that a randomly selected Christian living in the United States would identify as Catholic?

1. 0.659
2. 0.707
3. 0.208
4. 0.294

Question 7Select one answer.10 points

The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:

x	0	1	2	3	4	5
P(X = x)	0.20	0.30	0.20	0.15	0.10	0.05

What is the probability that in a given week there will be at most 3 accidents?

1. 0.70
2. 0.85
3. 0.35
4. 0.15
5. 1.00

Question 8Select one answer.10 points

The following three histograms represent the probability distributions of the three random variables X, Y, and Z.

Which of the three random variables has the largest standard deviation?

1. X
2. Y
3. Z
4. All three random variables have the same standard deviation.