Question 1

Still strange dice • The six faces of Die A show a 1 and five 3's. • Die B has four 2's and
two 6's.
Suppose you use these two dice in a competition against another player. You will roll one
of the dice and your opponent will roll the other one. The winner is the person who rolls
the higher number. You get first choice of dice and want to win. Would you pick Die A or
Die B? Explain why.

Accepted Answer

The answer of Still strange dice • The six faces...

Question 2

Given that a randomly selected bike has a kickstand, what are the chances that it also has a water Bottle holder?
A) 26%
B) 61.8%
C) 34%
D) 56.7%

Accepted Answer

The probability of a bike having a kickstand is 61.8%.

Question 3

If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)
A) 37.2, 6.34
B) 36, 3.14
C) 37.2, 2.24
D) 36, 8.88
E) none of these

Accepted Answer

The answer of If the restaurant is open for 8...

Question 4

We can tell that these two features are independent because…
A) The probability of having a kickstand given that you have a water bottle (56.7%) is about
equal to the probability of having a kickstand (55%).
B) These two features don't have anything to do with each other, so we know they're
independent.
C) The probability of having both features (34%) does not equal the probability of having neither
feature (19%).
D) The probability of having both features is not zero; it is 34%.
E) The probability of having either feature (81%) doesn't equal the probability of having just one
feature (60% and 55%).

Accepted Answer

The answer of We can tell that these two features...

Question 5

Shoot You and a friend are working on shooting free throws at basketball practice. Your
friend has a season average of making 80% of his shots.
a. If the coach asks your friend to shoot 70 times, how many shots do you expect him to
make, on average?
b. What is the standard deviation of the number of shots made out of 70?
c. Your friend makes 60 out of 70 shots and is ready to tell the coach that he is improving.
The graph below shows a simulation of this distribution. Using both your answers to (a)
and (b) and this graph, explain whether or not the coach should have confidence in his
improvement.

Accepted Answer

The answer of Shoot You and a friend are working...

Question 6

If my dresser drawer has 10 blue socks and 12 black socks and I randomly pull out two socks, what
Are the chances that they are both black?
A) 52%
B) 27.3%
C) 28.6%
D) 29.8%
E) none of these

Accepted Answer

The answer of If my dresser drawer has 10 blue...

Question 7

The length of a cat's tail is roughly normally distributed with a mean of 5" and a standard deviation
Of 2". The probability of having a cat with a 3.5" tail or shorter is…
A) 25%
B) 77.3%
C) 75%
D) 22.7%
E) none of these

Accepted Answer

The z-score for a 3.5" tail is (3.5 - 5) / 2 = -0.75. Using the standard normal distribution table, the probability of a z-score less than -0.75 is approximately 22.7%.

Question 8

If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances
of rolling exactly three successes?
A) 32.15%
B) none of these
C) 16.67%
D) 33.33%
E) 0.32%

Accepted Answer

The answer of If a 6-sided die is rolled 5...

Question 9

Cool Off A survey of southern California houses in a given town shows that 70% of the
homes have an air conditioning system and 90% of home have at least one ceiling fan. 65%
of all homes surveyed had both features.
a. What is the probability that a randomly selected home neither feature?
b. What is the probability that a randomly selected home has a ceiling fan, given that it
already has an air conditioning system?
c. Do these two house features appear to be independent? Justify your answer.

Accepted Answer

The answer of Cool Off A survey of southern California...

Question 10

What is the probability that a randomly selected bicycle will have a kickstand or a water bottle
Holder?
A) 61.8%
B) 56.7%
C) 34%
D) none of these
E) 81%

Accepted Answer

The answer of What is the probability that a randomly...

Question 11

Describe how you will use a random number table to conduct this simulation.

Accepted Answer

The answer of Describe how you will use a random...

Question 12

Growth A scientist is running an experiment that involves waiting for a culture to grow.
The average time for one experiment to run is 93 minutes with a standard deviation of 10
minutes.
a. If the scientist is going to run five experiments, with a 7 minute set-up time in between
each experiment, what is the average of the total time this will take?
b. What is the standard deviation of the total time?
c. What assumption did you need make the calculations in the previous two problems?

Accepted Answer

The answer of Growth A scientist is running an experiment...

Question 13

If the workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?
A) $46.50
B) none of these
C) $45
D) $4.65
E) $180

Accepted Answer

The answer of If the workers are paid $10/hour, what...

Question 14

Carpet A store selling carpet tracks the amount of square footage sold to its customers,
rounding to the nearest 500 sq. ft. Here is the distribution. $$\begin{array} { | l | l | l | l | l | } 
\hline \text { area } & 500 \text { sq. ft. } & 1000 \text { sq. ft. } & 1500 \text { sq. ft. } & 2000 + \text { sq. ft. } \
\hline \text { probability } & 0.10 & 0.25 & 0.45 & 0.20 \
\hline
\end{array}$$ 
a. What is the average expected area sold?
b. If the average cost of carpet sold is $3/sq. ft., what is the average sale price per customer?
c. If a salesman completes sales to five customers one day, what do you expect his total
sales to be?

Accepted Answer

The answer of Carpet A store selling carpet tracks the...

Question 15

Decorate A store sells ornaments for Christmas trees. The prices of the ornaments are
roughly normally distributed with a mean of $7.65 and a standard deviation of $1.45.
a. What is the probability that a randomly selected ornament will cost more than $10?
b. If eight ornaments are randomly selected, what is the probability that exactly 3 of them
cost over $10?

Accepted Answer

The answer of Decorate A store sells ornaments for Christmas...

Question 16

Which of these random variables has a binomial model?
A) The number of children a family has until they have two boys.
B) The number of girls a family has out of the three children they will have.
C) The number of times a free throw is shot until one shot is made.
D) The number of books we select out of a pile of 9 books that are non-fiction.
E) none of these

Accepted Answer

A binomial model is appropriate for a fixed number of independent trials, each with two possible outcomes (success or failure). Choice B fits this as it involves a fixed number of trials (three children) with two outcomes (girl or not a girl).

Question 17

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of Pulling out at least one green candy in three tries is… 
A) none of these
B) $( 0.85 ) ^ { 2 } ( 0.15 )$
C) $\left( \begin{array} { l } 3 \ 1 \end{array} \right) ( 0.15 ) ^ { 1 } ( 0.85 ) ^ { 2 }$
D) $1 - ( 0.85 ) ^ { 3 }$
E) $1 - ( 0.15 ) ^ { 3 }$

Accepted Answer

The probability of not pulling a green candy in one try is 0.85. The probability of not pulling a green candy in three tries is $(0.85)^3$. Therefore, the probability of pulling at least one green candy in three tries is $1 - (0.85)^3$.

Question 18

Describe how you will use a random number table to conduct this simulation.

Accepted Answer

The answer of Describe how you will use a random...

Question 19

State your conclusion.

Accepted Answer

The answer of State your conclusion....

Question 20

Show three trials by clearly labeling the random number table given below. Specify the
outcome of each trial. Trial 1:
10242506921897728370826698323677479906184370778695
Trial 2:
81183485546080939996819152540433366920820482279866
Trial 3:
06765670412047954612134113683769983530824358927865

Accepted Answer

The answer of Show three trials by clearly labeling the...

Quiz 8: Regression, Associations, and Predictive Modeling

Given that a randomly selected bike has a kickstand, what are the chances that it also has a water Bottle holder?

If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)

If my dresser drawer has 10 blue socks and 12 black socks and I randomly pull out two socks, what Are the chances that they are both black?

The length of a cat's tail is roughly normally distributed with a mean of 5" and a standard deviation Of 2". The probability of having a cat with a 3.5" tail or shorter is…

If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances of rolling exactly three successes? A) 32.15% B) none of these C) 16.67% D) 33.33% E) 0.32%

What is the probability that a randomly selected bicycle will have a kickstand or a water bottle Holder?

Describe how you will use a random number table to conduct this simulation.

If the workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?

Which of these random variables has a binomial model?

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of Pulling out at least one green candy in three tries is…

Describe how you will use a random number table to conduct this simulation.

State your conclusion.

Show three trials by clearly labeling the random number table given below. Specify the outcome of each trial. Trial 1: 10242506921897728370826698323677479906184370778695 Trial 2: 81183485546080939996819152540433366920820482279866 Trial 3: 06765670412047954612134113683769983530824358927865