1. Determine whether the following value is a continuous random variable, discrete random variable, or not a random
variable.
a. The number of statistics students now doing their homework
b. The last book a person in City A read
c. The number of free-throw attempts before the first shot is missed
d. The number of pigeons in a country
e. The number of runs scored during a baseball game
f. The amount of rain in City A during July
a. Is the a discrete random variable, continuous random
variable, or not a random variable?
number of statistics students now doing their homework
A. It is a continuous random variable.
B. It is a discrete random variable.
C. It is not a random variable.
b. Is the a discrete random variable, continuous random variable, or not a random
variable?
last book a person in City A read
A. It is a discrete random variable.
B. It is a continuous random variable.
C. It is not a random variable.
c. Is the a discrete random variable, continuous
random variable, or not a random variable?
number of free-throw attempts before the first shot is missed
A. It is a continuous random variable.
B. It is a discrete random variable.
C. It is not a random variable.
d. Is the a discrete random variable, continuous random variable, or not a random
variable?
number of pigeons in a country
A. It is a discrete random variable.
B. It is a continuous random variable.
C. It is not a random variable.
e. Is the a discrete random variable, continuous random variable, or
not a random variable?
number of runs scored during a baseball game
A. It is a continuous random variable.
B. It is a discrete random variable.
C. It is not a random variable.
f. Is the a discrete random variable, continuous random variable, or not a
random variable?
amount of rain in City A during July
A. It is a continuous random variable.
B. It is a discrete random variable.
C. It is not a random variable.
2.
YOU ANSWERED: A
B
B
A
C
Let the random variable x represent the number of girls in a family with three children.
Assume the probability of a child being a girl is . The table on the right describes the
probability of having x number of girls. Determine whether the table describes a probability
distribution. If it does, find the mean and standard deviation. Is it unusual for a family of
three children to consist of three girls?
0.31
x P(x)
0 0.329
1 0.443
2 0.199
3 0.029
Find the mean of the random variable. Select the correct choice below and, if necessary, fill in the answer box to
complete your choice.
A. ? =
(Round to two decimal places as needed.)
B. The table is not a probability distribution.
Find the standard deviation of the random variable. Select the correct choice below and, if necessary, fill in the
answer box to complete your choice.
A. ? =
(Round to two decimal places as needed.)
B. The table is not a probability distribution.
Is it unusual for a family with three children to have only girls?
A. No, because the probability of having 3 girls is greater than 0.05.
B. Yes, because the probability of having 3 girls is greater than 0.05.
C. No, because the probability of having 3 girls is less than or equal to 0.05.
D. Yes, because the probability of having 3 girls is less than or equal to 0.05.
3.
1: More Info
2: More Info
The accompanying table describes results from eight offspring peas. The random variable x represents the number
of offspring peas with green pods. Complete parts (a) through (d).
Click the icon to view the data.
2
a. Find the probability of getting exactly 7 peas with green pods.
(Type an integer or a decimal.)
b. Find the probability of getting 7 or more peas with green pods.
(Type an integer or a decimal.)
c. Which probability is relevant for determining whether 7 is an unusually high number of peas with green pods, the
result from part (a) or part (b)?
The result from part (b)
The result from part (a)
d. Is 7 an unusually high number of peas with green pods? Why or why not? Use 0.05 as the threshold for an
unusual event.
A. No, since the appropriate probability is greater than 0.05, it is not an unusually high number.
B. Yes, since the appropriate probability is less than 0.05, it is an unusually high number.
C. No, since the appropriate probability is less than 0.05, it is not an unusually high number.
D. Yes, since the appropriate probability is greater than 0.05, it is an unusually high number.
Probabilities of Numbers of Peas with
Green Pods Among 8 Offspring Peas
x (Number of Peas
with Green Pods) P(x)
0 0+
1 0+
2 0.006
3 0.027
4 0.093
5 0.244
6 0.278
7 0.249
8 0.103
4.
5.
Probabilities of Numbers of Peas with
Green Pods Among 8 Offspring Peas
x (Number of Peas
with Green Pods) P(x)
0 0+
1 0+
2 0.006
3 0.027
4 0.093
5 0.244
6 0.278
7 0.249
8 0.103
In a state’s Pick 3 lottery game, you pay $ to select a sequence of three digits (from 0 to 9), such as . If you
select the same sequence of three digits that are drawn, you win and collect $ . Complete parts (a) through
(e).
1.23 199
320.68
a. How many different selections are possible?
b. What is the probability of winning?
(Type an integer or a decimal.)
c. If you win, what is your net profit?
$ (Type an integer or a decimal.)
d. Find the expected value.
$ (Round to the nearest hundredth as needed.)
e. If you bet in a certain state’s Pick 4 game, the expected value is . Which bet is better, a $ bet
in the Pick 3 game or a bet in the Pick 4 game? Explain.
$1.23 ? $0.91 1.23
$1.23
A. Neither bet is better because both games have the same expected value.
B. The Pick 4 game is a better bet because it has a larger expected value.
C. The Pick 3 game is a better bet because it has a larger expected value.
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the
requirements that are not satisfied.
Surveying 50 college students and asking if they like pirates or ninjas better, recording Yes or No
Choose the correct answer below.
A. Yes, because all 4 requirements are satisfied.
B. No, because there are more than two possible outcomes.
C. No, because there are more than two possible outcomes and the trials are not independent.
D. No, because the probability of success does not remain the same in all trials.
6.
7.
8.
Determine whether the following probability experiment represents a binomial experiment and explain the reason
for your answer.
cards are selected from a standard 52card deck without replacement. The number of selected is
recorded.
Five fours
Does the probability experiment represent a binomial experiment?
A. No, because there are more than two mutually exclusive outcomes for each trial.
B. No, because the experiment is not performed a fixed number of times.
C. Yes, because the experiment satisfies all the criteria for a binomial experiment.
D. No, because the trials of the experiment are not independent and the probability of success
differs from trial to trial.
Determine whether or not the procedure described below results in a binomial distribution. If it is not binomial,
identify at least one requirement that is not satisfied.
hundred different voters in a region with two major political parties, A and B, are randomly selected from the
population of registered voters. Each is asked if he or she is a member of political party A, recording Yes or
No.
Five
7000
Choose the correct answer below.
A. No, the trials are not independent and the sample is more than 5% of the population.
B. No, there are more than two possible outcomes.
C. No, the probability of success is not the same in all trials.
D. Yes, the result is a binomial probability distribution.
E. No, the number of trials is not fixed.
Multiplechoice questions each have possible answers , one of which is correct. Assume that you
guess the answers to three such questions.
four (a, b, c, d)
a. Use the multiplication rule to find P(WCW), where C denotes a correct answer and W denotes a wrong answer.
P(WCW) = (Type an exact answer.)
b. Beginning with , make a complete list of the different possible arrangements of correct and
wrong , then find the probability for each entry in the list.
WCW one answer
two answers
P(WCW) ? see above
P(CWW) =
P(WWC) =
(Type exact answers.)
c. Based on the preceding results, what is the probability of getting exactly correct when three guesses
are made?
one answer
(Type an exact answer.)
9.
3: Binomial Distribution Table
4: Binomial Distribution Table
Assume that a procedure yields a binomial distribution with n trials and a probability of success of p . Use
a binomial probability table to find the probability that the number of successes x is exactly .
= 5 = 0.30
2
Click on the icon to view the binomial probabilities table.
4
P(2) = (Round to three decimal places as needed.)10.
5: Binomial Distribution Table
Assume that a procedure yields a binomial distribution with trials and a probability of success of . Use a
binomial probability table to find the probability that the number of successes is exactly .
6 0.30
6
Click on the icon to view the binomial probability table.
6
The probability that the number of successes is exactly 6 is .
(Round to three decimal places as needed.)
6: Binomial Distribution Table
11.
12.
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial.
n = 5, x = 3, p = 0.55
P(3) = (Round to three decimal places as needed.)
In a region, there is a probability chance that a randomly selected person of the population has brown eyes.
Assume people are randomly selected. Complete parts (a) through (d) below.
0.95
12
a. Find the probability that all of the selected people have brown eyes.
The probability that all of the 12 selected people have brown eyes is .
(Round to three decimal places as needed.)
b. Find the probability that exactly 11 of the selected people have brown eyes.
The probability that exactly 11 of the selected people have brown eyes is .
(Round to three decimal places as needed.)
c. Find the probability that the number of selected people that have brown eyes is 10 or more.
The probability that the number of selected people that have brown eyes is 10 or more is .
(Round to three decimal places as needed.)
d. If 12 people are randomly selected, is 10 an unusually high number for those with brown eyes?
A. , because the probability that or more of the selected people have brown eyes is than
0.05.
No 10 less
B. , because the probability that or more of the selected people have brown eyes is
than 0.05.
No 10 greater
C. , because the probability that or more of the selected people have brown eyes is
than 0.05.
Yes 10 less
D. , because the probability that or more of the selected people have brown eyes is
than 0.05.
Yes 10 greater
13.
14.
15.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to
randomly select and test tablets. The entire shipment is accepted if at most 2 tablets do not meet the required
specifications. If a particular shipment of thousands of aspirin tablets actually has a % rate of defects, what is
the probability that this whole shipment will be accepted?
10
3.0
The probability that this whole shipment will be accepted is .
(Round to three decimal places as needed.)
Several psychology students are unprepared for a surprise true/false test with questions, and all of their
answers are guesses.
11
a. Find the mean and standard deviation for the number of correct answers for such students.
b. Would it be unusual for a student to pass by guessing (which requires getting at least correct answers)? Why
or why not?
8
a. ? =
? = (Round to one decimal place as needed.)
b. Choose the correct answer below.
A. Yes, because 8 is greater than the maximum usual value.
B. No, because 8 is within the range of usual values.
C. Yes, because 8 is within the range of usual values.
D. Yes, because 8 is below the minimum usual value.
a. For classes of students, find the mean and standard deviation for the number born on the 4th of July.
Ignore leap years.
119
b. For a class of 119 students, would two be an unusually high number who were born on the 4th of July?
a. The value of the mean is ? = .
(Round to six decimal places as needed.)
The value of the standard deviation is ? = .
(Round to six decimal places as needed.)
b. Would 2 be an unusually high number of individuals who were born on the 4th of July?
A. This result is unlikely because 2 is within the range of usual values.
B. No, because 2 is within the range of usual values.
C. Yes, because 2 is below the minimum usual value.
D. Yes, because 2 is greater than the maximum usual value.
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