Week 6 | Complete Solution

_____1. Ten different senators are randomly selected without replacement, and the
number of terms that they have served are recorded. Does this constitute a binomial distribution?
Select an answer, and then state why.
a. No
b. Yes
Why: 

_____2. Which of the following pairs are NOT independent events?
a. Flipping a coin and getting a head, then flipping a coin and getting a tail
b. Throwing a die and getting a 6, then throwing a die and getting a 5
c. Selecting a red marble from a bag, returning the marble to the bag, then selecting a blue
marble
d. Drawing a spade from a set of poker cards, setting the card aside, then selecting a
diamond from the set of poker cards
e. All of the above are independent events 
_____3. Exam scores from a previous STATS 200 course are normally distributed with a
mean of 74 and standard deviation of 2.65. Approximately 95% of its area is within:
a. One standard deviation of the mean
b. Two standard deviations of the mean
c. Three standard deviations of the mean
d. Depends on the number of outliers
e. Must determine the z-scores first to determine the area

_____4. You had no chance to study for the final exam and had to guess for each
question. The instructor gave you three choices for the final exam:
I: 10 questions, each question has 5 choices, must answer at least 4 correct to pass
II: 5 questions, each question has 4 choices, must answer at least 3 correct to pass
III: 4 questions, each question has 6 choices, must answer at least 2 correct to pass
Which final exam format offers the highest probability to pass?
a. Final exam I
b. Final exam II
c. Final exam III
d. All three final formats have equal probabilities
e. Need more information to compute probabilities 
_____5. Consider a normal distribution with a mean of 12 and variance of 4.
Approximately 82% of the area lies between which values?
a. 6 and 13
b. 10 and 16
c. 9 and 15
d. 10 and 18
e. Not enough information provided to solve

_____6. For a standard normal distribution, what’s the probability of getting a number
less than zero?
a. 75%
b. 63%
c. 50%
d. 43%
e. 34%

_____7. Which description of normal distributions is correct (select all that apply)?
a. Normal distributions have a mean of zero and standard deviation of one.
b. Normal distributions can differ in their means, but their standard deviations must be the
same.
c. Standard normal distributions cannot differ in both their means and their standard
deviations.
d. Normal distributions cannot differ in their means, but can differ in their standard
deviations.
e. None of the above are correct

_____8. Consider an extremely right skewed distribution with a mean of 15 and standard
deviation of 2. 99.7% of its area is within:
a. One standard deviation of the mean
b. Two standard deviations of the mean
c. Three standard deviations of the mean
d. 2.5 standard deviations of the mean
e. Can’t determine from the information given.

_____9. A delivery truck must make stops in eight different cities, designated by the first
letter in the name of the city: A, B, C, D, E, F, G, and H. If the order in which the truck visits the
eight locations is chosen randomly, what is the probability that the truck will visit them in reverse
alphabetical order?

    (8^C 1)/(8^P 1)                b.  1/(8^P 8)            c.  1/(8^C 8)           d.  (8^P 1)/(8^C 1)

_____10. Acme Airlines fly’s airplanes that seat 100 passengers. From experience, they
have determined, on average, 84% of the passengers holding reservations for a particular flight
actually show up for the flight. If they book 116 passengers for a flight, what is the probability
(rounded to four decimals) that 100 or fewer passengers holding reservations will actually show
up for the flight?

a. 0.8400     b. 0.8590     c. 0.8621     d. 0.7774     e. 0.7241 
_____11. A jar contains 12 marbles, 5 of which are green and 7 of which are blue. If 2
marbles are chosen at random (without replacement) and then 2 additional marbles are chosen at
random (without replacement), what is the probability of selecting 3 green marbles and 1 blue
marble?

     (5^C 3  ·  7^C 1)/(〖12〗^C 4)    b.  (5^P 3  ·  7^P 1)/(〖12〗^P 4)        c.  (5^C 2  ·  7^P 2)/12        d.  (5^C 3  ·  7^P 1)/12

_____12. If events A and B are mutually exclusive events, each with non-zero probability, then which of the following is true: 

a. P(A ∩ B) = P(A) + P(B) 
b. P(A ∪ B) = P(A) + P(B) 
c. P(A) – 1 = P(B) 
d. P(A) = P(B) 
e. P(A ∩ B) = P(A)*P(B)

13. An elevator has a stated maximum capacity of 12 people or 2004 pounds. If 12
people have weights with a mean greater than (2004/12) = 167 pounds, the capacity will be
exceeded. Assume that weights of men are normally distributed with a mean of 182.9 pounds
and a standard deviation of 40.8 pounds. Show your work and round your answers to FOUR
decimal places.

a. Compute the probability that a randomly selected man will have a weight greater than
167 pounds.

b. Compute the probability that 12 randomly selected men will have a mean weight that is
greater than 167 pounds.

c. Does the elevator appear to have the correct weight limit? Why or why not?

14. A company has initiated a training program for new hires. After surveying 25 new
employees, they determined the average training time was 7.5 hours with a sample standard
deviation of 2.25 hours. Assume that the underlying population is normally distributed. Show
your work and round your CI to FOUR decimal places.

a. Define the random variable X for this problem in words.

b. Define the random variable 𝑋̅ for this problem in words.

c. Construct a 95% confidence interval for the population mean length of time of new hire
training. 
d. A new employee scheduled for the training program, stated he would only need 6 hours
to complete the training. Is his claim reasonable? State why or why not.

15. A researcher randomly surveyed 300 high school seniors and determined 225 stated they drive a car to high school. We are interested in the population proportion of seniors who drive a car to high school.
a. Define the random variable X for this problem in words.

b. Define the random variable P’ for this problem in words.

c. Construct a 90% confidence interval (CI) for the population proportion of high school
seniors who claim to drive a car to high school. Round your CI to FOUR decimal places.

d. Is it reasonable to conclude at least 80% of seniors drive a car to high school?