Question 1

The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let's call X the number of color-blind individuals in a random sample of 8 Caucasian American males. The table gives the probability distribution for X.
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline P ( X ) & 0.513 & 0.357 & 0.109 & 0.019 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \
\hline
\end{array}$$ What is the probability of getting at least 6 color-blind individuals in the sample?

Accepted Answer

A) 0.000 
B) 0.333 
C) 0.375 
D) 1.000

Question 2

What is the term for a variable whose value is a numerical outcome of a random phenomenon?

Accepted Answer

A) Random variable 
B) Parameter 
C) Biased 
D) Random sample

Question 3

Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse, as defined in the official psychiatric manual. Choose a young person (age 19 to 25) at random and ask, "In the past seven days, how many days did you watch television?" Call the response X for short. Here is a probability model for the response:
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline \text { Days } X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Probability } & 0.04 & 0.03 & 0.06 & 0.08 & 0.09 & 0.08 & 0.05 & ? \
\hline
\end{array}$$ What is the correct notation for "watched TV at least two days in the past week" in terms of X?

Accepted Answer

A) X > 1 
B) X > 2 
C) X = 2 
D) X < 1

Question 4

The Centers for Disease Control and Prevention receives information about the causes for HIV/AIDS infection in the United States. Here are the causes of infection and their respective probability among American women age 20 to 24 years:
?
?
$\begin{array}{c}
\begin{array}{lll}
\bf{Cause}\
\text{Injection drug use} \
\text{Heterosexual sex} \
\text{Perinatal infection} \
\text{Other causes}
\end{array}
\begin{array}{lll}
\bf{Probability}\
? \
0.664 \
0.125 \
0.095
\end{array}
\end{array}$ What is the probability that an American woman age 20 to 24 contracted HIV/AIDS either via heterosexual sex or via perinatal infection?

Accepted Answer

A) 0.083 
B) 0.211 
C) 0.500 
D) 0.789

Question 5

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What are the odds of myopia in the 18- to 24-year-old American population?

Accepted Answer

A) 0.381 
B) 0.616 
C) 1.616 
D) 2.625

Question 6

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What is the probability that a randomly chosen American between the ages of 18 and 24 does NOT have myopia?

Accepted Answer

A) -0.381 
B) 0.381 
C) 0.616 
D) 0.619

Question 7

The probability density of a random variable X is given in the figure.
What is the probability that X = 1.5?

Accepted Answer

A) 0 
B) 1/4 
C) 1/3 
D) 1/2

Question 8

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, what is the probability of A or B?

Accepted Answer

A) 0.0 
B) 0.1 
C) 0.2 
D) 0.9

Question 9

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among American women age 20 to 24 is 2791.5 per 100,000. What are the approximate odds of a Chlamydia infection in the 20- to 24-year-old U.S. female population?

Accepted Answer

A) 0.0279 
B) 0.0287 
C) 0.2792 
D) 0.2872

Question 10

The probability density of a random variable X is given in the figure.
What is the value of P(0 < X ≤ 2)?

Accepted Answer

A) 0.0 
B) 0.5 
C) 1.0 
D) 2.0

Question 11

Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans.
​
​
 $$\begin{array} { | l | l | l | l | l | l | } 
\hline \boldsymbol { X } & 0 & 1 & 2 & 3 & 4 \text { or more } \
\hline \text { Probability } & 0.36 & 0.26 & 0.19 & 0.09 & ? \
\hline
\end{array}$$ What is the probability that an American does NOT consume 2 cups of coffee daily?

Accepted Answer

The answer of Based on a recent Gallup survey, we...

Question 12

Based on data from the U.S. Department of Agriculture, we define the following probability model for the number X of different pesticides detected in fresh produce.
​
​
 $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline X & 0 & 1 & 2 & 3 & 4 & 5 \text { or more } \
\hline \text { Probability } & 0.43 & 0.17 & 0.14 & 0.08 & 0.06 & 0.12 \
\hline
\end{array}$$ What is the numerical value for the probability P(X < 2)?

Accepted Answer

The answer of Based on data from the U.S. Department...

Question 13

Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse, as defined in the official psychiatric manual. Choose a young person (age 19 to 25) at random and ask, "In the past seven days, how many days did you watch television?" Call the response X for short. Here is a probability model for the response:
?
?
$$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline \text { Days } X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Probability } & 0.04 & 0.03 & 0.06 & 0.08 & 0.09 & 0.08 & 0.05 & ? \
\hline
\end{array}$$ For a randomly selected student, which of the following terms describes the events X = 3 and X = 4?

Accepted Answer

A) Disjoint 
B) Not disjoint 
C) Independent 
D) Complementary

Question 14

Which of the following defines an event considered to have an unusual probability?

Accepted Answer

A) The probability exceeds 1. 
B) The probability is a negative number. 
C) The probability is very low. 
D) The probability equals 1.

Question 15

The probability density of a random variable X is given in the figure.
What is the probability that X is at least 1.5?

Accepted Answer

A) 0 
B) 1/4 
C) 1/3 
D) 1/2

Question 16

What is the probability that an event will occur?

Accepted Answer

A) The number of successful outcomes divided by the number of unsuccessful outcomes 
B) The number of successful outcomes divided by the total number of outcomes 
C) The number of unsuccessful outcomes divided by the number of successful outcomes 
D) The number of unsuccessful outcomes divided by the total number of outcomes

Question 17

Studies indicate that approximately 7% of Americans are vegetarians. If an American is selected at random, what is the probability that he or she is NOT a vegetarian?

Accepted Answer

The answer of Studies indicate that approximately 7% of Americans...

Question 18

A physician observes the number of lesions on subjects who regularly used tanning salons. Let X be the number of lesions observed. The physician found that X had the following probability distribution.
?
?
$$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Value of } \boldsymbol { X } & 0 & 1 & 2 & 3 & 4 \
\hline \text { Probability } & 0.05 & 0.1 & 0.25 & 0.30 & 0.30 \
\hline
\end{array}$$ What is the probability that a randomly chosen subject has at least three lesions?

Accepted Answer

A) 0.3 
B) 0.4 
C) 0.6 
D) 0.7

Exam 8: Essential Probability Rules