Part 1 Multiple Choice:
The Gallup Poll interviewed 1423 randomly selected American citizens and reported that when asked which type of content bothers them most on TV, 44% identified ‘violence’. Answer the next two questions with this information.
1. Identify the population.
a. 1423
b. American citizens
c. Gallup poll
d. 44%
2. The 44% that identified ‘violence’ as what bothered them the most from the sample of 1423 randomly selected American citizens is called
a. a parameter
b. a statistic
c. Simpson’s paradox
d. None of these above
3. Fill in the blank: The ________ of a variable tells us what values it takes and how often it takes these values.
a. probability
b. distribution
c. population
d. variable
4. 85% of the phone calls to Regional Airways is for reservations. Suppose there were 100 calls to Regional Airways. Describe the distribution of the number of calls that were for reservations out of the 100.
a. Normal distribution with mean = 100, standard deviation = 85.
b. Binomial distribution with n = 100, p = 0.85.
c. Binomial distribution with mean = 100, standard deviation = 85.
d. Uniform distribution with n = 100, p = 0.85.
The city gas mileage for 2001 vehicles has a mean µ = 21.2 miles per gallon and standard deviation σ = 5.4 MPG. Let X be the city MPG of 2014 model year vehicles. Assume the gas mileage has an approximate Normal distribution. Answer the next two questions.
5. Find the probability that a vehicle chosen at random has a city MPG of 32 or higher.
a. 0.02
b. 0.9772
c. 0.0228
d. 0.108
6. Suppose that a simple random sample of 36 vehicles were selected. What is the probability that the sample mean MPG,![]()
, of these 36 vehicles is greater than 23 MPG?
a. 0.01
b. 0.8413
c. 0.9772
d. 0.0228
The table below shows quality ratings and the mean price from a sample of 300 restaurants located in the Los Angeles area. Use this information to answer the next three questions.
|
|
Meal Price
|
|
|
Quality Rating
|
$10 – 19
|
$20 – 29
|
$30 – 39
|
$40 – 49
|
Total
|
|
Good
|
42
|
40
|
2
|
0
|
84
|
|
Very Good
|
34
|
64
|
46
|
6
|
150
|
|
Excellent
|
2
|
14
|
28
|
22
|
66
|
|
Total
|
78
|
118
|
76
|
28
|
300
|
7. What is the percent of “Good” Quality Rating?
a. 28%
b. 26%
c. 53.8%
d. 0%
8. What percent of the restaurants have a “Good” rating and has a meal price between $30 – 39?
a. 2.4%
b. 3%
c. 0.67%
d. 28%
9. What percent of the restaurants have an “Excellent” rating, given that the meal price is $40 – 49?
a. 7.3%
b. 78.6%
c. 33.3%
d. 22%
Assume that 10% of people are left-handed. We randomly select 20 people at random. Answer the next two questions
10. What is the probability that exactly 5 out of the 20 people are left-handed?
a. 0.25
b. 0.032
c. 0
d. 0.98875
11. What is the expected number of left-handed people out of the 20 randomly selected?
Employment data at a large company reveal that 72% of the workers are married, 40% are college graduated, and that 45% are married, given that they are college graduates. Let C be the event that a selected worker is college graduated, M be the event that a worker is married. According to this large company P(M) = 0.72, P(C) = 0.4 and P(M|C) = 0.45. Answer the next three questions using this information. (Hint: The Venn diagram might be helpful.)
12. What is the probability that a randomly chosen worker is married and a college graduate?
a. 0.18
b. 0.3168
c. 0.45
d. 0.67
13. What is the probability that a randomly chosen worker is married or a college graduate?
a. 0.14
b. 1.12
c. 0.67
d. 0
14. Fill in the blank: Married and college graduated are ______________ events.
a. Disjoint
b. Independent
c. Both a and b
d. Neither a nor b
A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 ml. In fact, the contents vary according to a Normal distribution with mean µ = 298 and standard deviation σ = 3 ml. Suppose the company is looking at the mean content of 6-pack bottles. Answer the next two questions.
15. What is the mean and standard deviation of the sample mean, ![]()
, of the 6-pack bottles?
16. What is the probability that the mean contents of bottles in a six – pack(6 cans) is less than 295 ml?
a. 0.1587
b. 0.0071
c. 0.8413
d. 0.9929
A box is filled with 20 marbles, 10 are red, 5 are blue, 3 are yellow and 2 are green. Answer the next two questions.
17. If one marble is drawn from the box, what is the probability that the marble is yellow or green?
a) 0.25
b) 0.10
c) 0.015
d) 0.15
18. If two marbles are drawn from the box without replacement, what is the probability of drawing a yellow marble first and a green marble second?
a) 0.25
b) 0.15
c) 0.016
d) 0.90
19. Find the area under a standard Normal curve that is in the interval -1.6 < z < 2.9.
a) 0.0548
b) 0.0529
c) 0.9981
d) 0.9433
20. Which of the following best describes the shape of a Normal distribution?
a) skewed
b) symmetric
c) uniform
d) presence of outliers
Part 2 Problem Solving: Show all your work, partial credit may be given for proper work. Put your answer in the blank provided.
Problem 1: Wendy enjoys a certain gambling game at the casino. X = her profit in dollars from one round of the game. The probability distribution of X is listed in the table below.
|
Profit X
|
-$1
|
$1
|
$3
|
|
Probability
|
0.5
|
0.3
|
0.2
|
a) What is the probability that Wendy wins money in one game? That is her profit is positive in one game?
b) What is the probability that Wendy wins money in three consecutive rounds?
c) If Wendy plays three times what is the probability that she wins money at least one time?
d) What is the mean winning![]()
?
e) What is the standard deviation of the winnings?
Problem 2: The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.
a) What is the probability that a length of pregnancy will last less than 200 days?
b) What is the probability that the length of a pregnancy will last more than 246 days?
c) What percent of pregnancies last between 234 days and 298 days?
d) How long do the longest 10% of pregnancies last?
Problem 3: 16% of executive job applicants lied on their resumes. Suppose an executive job hunter randomly selects 10 resumes from an executive job application pool.
a) What is the probability that exactly 5 out of the 10 were misleading resumes?
b) What is the probability that at least one resume was misleading?
c) What is the expected value of misleading resumes from the 10?
d) What is the standard deviation of the number of misleading resumes?
