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Probability and Random Variables Review

Total questions: 17

Worksheet time: 26mins

Name
Class
Date
1.
A company states that 2% of its computers are returned for defects.  We take a sample of 100 computers to find the probability of 10 being defective.  Is this a binomial distribution?
a)
No because there is not a fixed number of trials.
b)
No because their are more than 2 outcomes.
c)
Yes since there are a fixed number of independent trials, outcomes in 2 categories, and the probability of defect is constant.
d)
No since computers would not be independent.
2.
A September 2011 Gallup survey suggests that 38% of Americans are planning on voting for Barack Obama in the 2012 presidential election. Among a random sample of 100 people, approximately how many would you expect to vote for Obama? 
a)
38 people
b)
42 people
c)
6 people
d)
Cannot be determined
3.
The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood? 
a)
0.088
b)
0.697
c)
0.214
d)
0.303 
4.
The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that the tenth blood donor is the first donor with Type B blood?
a)
approximately 0.00
b)
0.316
c)
0.0385 
d)
0.279
5.
What is the probability that a student does play a sport given they do not play an instrument? 
a)
.2
b)
.2222
c)
.10
d)
.5
6.

Find P(Male ∪\cup  Sports Car)

a)

60240\frac{60}{240}  

b)

84240\frac{84}{240}  

c)

105240\frac{105}{240}  

d)

144240\frac{144}{240}  

e)

39240\frac{39}{240}  

7.

Which of the following random variables is discrete?

a)

The number of shots made in 10 free-throw attempts.

b)

The weight of a rhinoceros.

c)

The species of an insect.

d)

The length of a needle on a saguaro cactus.

e)

None of the variables above are discrete.

8.

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The expected value of X is E(X) =

a)

0.40

b)

1.00

c)

1.45

d)

1.66

e)

2.50

9.

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The standard deviation of X is 1.27. Interpret this value.

a)

The number of computers in a randomly selected household is within 1.27 of the mean.

b)

The number of computers in a randomly selected household is exactly 1.27 from the mean.

c)

The number of computers in a randomly selected household is 1.27, on average.

d)

The number of computers in a randomly selected household is typically 1.27 from the mean.

e)

The average number of computers in a randomly selected household is typically 1.27 from the mean.

10.

The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32.

Select two days at random and find the difference in the number of DVDs rented on the two days. What are the mean and standard deviation of the difference in the number of DVDs rented?

a)

Mean = 0, Standard Deviation = 0

b)

Mean = 0, Standard Deviation = 64

c)

Mean = 0, Standard Deviation = 45

d)

Mean = 92, Standard Deviation = 32

e)

Mean = 134, Standard Deviation = 32

11.

Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?

a)

X = student’s height; Y = student’s weight

b)

X = student’s IQ; Y = student’s GPA

c)

X = student’s PSAT Math score; Y = student’s PSAT Verbal score

d)

X = average amount of homework the student does per night; Y = student’s GPA

e)

X = average amount of homework the student does per night; Y = student’s height

12.

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital’s capacity will be exceeded?

a)

0.011

b)

0.965

c)

0.035

d)

0.989

e)

0.092

13.

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean = 10 ounces and standard deviation  = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

a)

Normal, with mean 10 ounces and standard deviation 1 ounce.

b)

Normal, with mean 40 ounces and standard deviation 2 ounces

c)

Normal, with mean 40 ounces and standard deviation 4 ounces

d)

binomial, with mean 40 ounces and standard deviation 2 ounces

e)

binomial, with mean 40 ounces and standard deviation 4 ounces.

14.

The mean amount of time to mix the batter for a cake is 14 minutes with a standard deviation of 2.5 minutes. The mean amount of time to bake the cake is 35 minutes with a standard deviation of 6.2 minutes. What is the mean time to make and bake a cake? What is the standard deviation?

a)

mean = 49 min sd = 8.7 min

b)

mean = 49 min sd = 6.685 min

c)

mean = 21 min sd = 8.7 min

d)

mean = 21 min sd = 6.685 min

15.
In a particular game, a fair die is tossed.  If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing.  Let X be the amount that you win. 
Which of the following is the expected value of X?
a)
$1.00
b)
$2.50
c)
$4.00
d)
$6.00
16.

When you add a positive constant to a random variable the effects on the random variables distribution are as follows:

a)

the shape is changed, the mean is increased by a value of "a" and the standard deviation is unchanged.

b)

the shape and standard deviation are unchanged and the mean is increased by a value of "a".

c)

all three aspects are unchanged

d)

the shape and mean are unchanged and the standard deviation is increased by a value of "a".

17.

Multiplying a random variable by a positive constant "b" affects the distribution of the random variable as follows:

a)

the shape is unchanged, measures of center and spread, both, are multiplied by "b".

b)

the shape, measures of center and measures of spread are all multiplied by "b".

c)

the shape and measures of center are unchanged, the measures of center are multiplied by "b".

d)

there is no change in the distribution.

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