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Do not open and start the exam until instructed to do so.
P( A | B) 
P( A AND B)
P( B)
SE =
P(A|B) = P(A)
P(A AND B) = P(A)P(B)
P(Ac) = 1 – P(A)
P(A OR B) = P(A) + P(B) – P(A AND B)
p(1- p)
n
Exam 2 – Math 140
Each question is worth 3 points
Form A
1. When two fair six-sided dice are simultaneously thrown, these are two of the possible results that could occur: Result 1: a 5 and a 6
are obtained in any order. Result 2: a 5 is obtained on each die. Which of the following statements is correct?
a. The probability of obtaining each of these results is equal.
b. There is a higher probability of obtaining Result 1 (a 5 and a 6 in any order).
c. There is a higher probability of obtaining Result 2 (a 5 on each die).
d. It is impossible to give an answer, because the throws of the dice aren’t independent.
e. None of the above.
2. Suppose you read on the back of a lottery ticket that the chances of winning a prize are 1 out of 10. Select the best interpretation.
a. You will win at least once out of the next 10 times you buy a ticket.
b. You will win exactly once out of the next 10 times you buy a ticket.
c. You might win once out of the next 10 times, but it is not for sure.
d. You will not win exactly 9 out of the next 10 times you buy a ticket.
e. It’s impossible to determine without knowing how many lottery tickets were sold.
3. A game company created a little plastic dog that can be tossed in the air. It can land either with all four feet on the ground, lying on
its back, lying on its right side, or lying on its left side. However, the company does not know the probability of each of these
outcomes. They want to estimate the probabilities. Which of the following methods is most appropriate?
a. Since there are four possible outcomes, assign a probability of 2/4 to each outcome.
b. Toss the plastic dog many hundreds of times and see what percent of the time each outcome occurs.
c. Simulate the data using a model that has four equally likely outcomes.
d. Since there are four possible outcomes, assign a probability of 1/4 to each outcome.
e. Toss the plastic dog 10 times and see what percent of the time each outcome occurs.
4. The local Meteorologist claims that there is a 70% probability of rain tomorrow. Provide the best interpretation of this statement.
a. Approximately 70% of the city will receive rain within the next 24 hours.
b. Historical records show that it has rained on 70% of previous occasions with the same weather conditions.
c. If we were to repeatedly monitor the weather tomorrow, 70% of the time it will be raining.
d. Over the next ten days, it should rain on seven of them.
e. Over the next ten days, it probably will rain on seven of them.
5. A doctor collects a large set of heart rate measurements that approximately follow a normal distribution. He only reports 3 statistics,
the mean = 110 beats per minute, the minimum = 65 beats per minute, and the maximum = 155 beats per minute. Which of the
following is most likely to be the standard deviation of the distribution?
a. 5
b. 15
c. 45
d. 20
e. 10
6. Which of the following statements are false?
I: The precision of an estimator does not depend on the size of the population.
II: The precision of an estimator does not depend on the size of the sample.
III: Surveys based on larger sample sizes have larger standard errors.
a. I only
b. I and II only.
c. II only.
d. I, II, and III.
e. II and III only.
7. Each of the 110 students in a statistics class selects a different random sample of 35 Quiz scores from a population of 5000
scores they are given. Using their data, each student constructs a 90% confidence interval for p, the proportion of the
5000 students who passed. Which of the following conclusions is correct?
a. About 10% of the sample proportions will not be included in the confidence intervals.
b. About 90% of the confidence intervals will contain p.
c. It is probable that 90% of the confidence intervals will be identical.
d. About 10% of the raw scores in the samples will not be found in these confidence intervals.
e. About 90% of the raw scores in the samples will not be found in these confidence intervals.
8. Which of the following characteristics are not required for the binomial model?
a. The probability of success and of failure must be equal.
b. There are a fixed number of trials.
c. The trials must be independent.
d. The probability of success is the same at each trial.
e. All of the above are required.
9. Suppose a normal model has a mean of 50, and 65% of the values are between 45 and 55. Which of the following must be
true about the standard deviation?
a. The standard deviation must be greater than 5.
b. The standard deviation must be less than 5.
c. The standard deviation must be exactly 5.
d. It is impossible for 65% of the values to be between 45 and 55.
e. There is not enough information to determine anything about the standard deviation.
10. What is the mean and standard deviation of the standard Normal Model?
a. The standard normal model has a mean of 1 and standard deviation of 1.
b. The standard normal model has a mean of 1 and standard deviation of 0.
c. The standard normal model has a mean of 0 and standard deviation of 0.
d. The standard normal model has a mean of 0 and standard deviation of 1.
e. None of the above.
11. What is the true shape of a binomial distribution?
a. The shape depends on both the number of trials, n, and the probability of success, p.
b. The shape is always the same.
c. The shape depends completely on the probability of success, p.
d. The shape depends completely on the number of trials, n.
e. The shape is independent of both the number of trials, n, and the probability of success, p.
12. What do you expect for the shape of the sampling distribution for sample proportions for all possible samples as the
sample size is increased? (Assume the CLT requirements are met)
a. Shaped more like a normal distribution.
b. Shaped more like the population distribution.
c. Shaped like neither the population distribution nor the normal distribution.
d. It is impossible to tell.
e. Shaped more like a binomial distribution.
13. What do you expect for the variability of a sampling distribution when the sample size is increased? (Assume the CLT
requirements are met)
a. More variability.
b. Less variability.
c. It is impossible to tell.
d. The mean of the sampling distribution should get closer to population parameter.
e. The variability will be the same as the population distribution.
14. In a simulation of coin tosses, a streak of 20 tails has appeared. The Law of Large Numbers says which of the following
must be true?
a. The 21st flip is less likely to come up tails.
b. The simulation was designed incorrectly.
c. The 21st flip is more likely to come up heads.
d. It is equally likely that the 21st toss will be a head or tail.
e. All of the above are true.
15. When reading about the findings of a survey, which of the following is not important to know?
a. Who conducted the survey.
b. Whether the researchers chose people to participate in the survey or people themselves chose to participate.
c. What percentage of people who were asked to participate actually did so.
d. How many questions were in the survey.
e. All of above are important to know.
Math 140
Exam 2A – Written
Name______________________________________________
CSUN ID___________________________________________
You must show all of your work or you get no credit.
1. A sampling method should be as precise and accurate as possible. Explain what these two terms mean and how each is
measured. (8 pts)
2. Suppose a deck of cards is shuffled and one card is dealt face-down on the table. Using the mathematical definition, show
that the events “the card is black” and “the card is a spade” are not independent. (7 pts.)
3. Roll a fair, six sided die. Find the probability that the die shows an odd number or a number less than 3 on top. (6 pts.)
4. Briefly explain the purpose of statistical inference. (5 pts.)
5. Suppose we are interested in the frequency that the letter E is used in the English language. A simple random sample
without replacement was taken from a modern day book. The sample consisted of 950 letters, and we found 110 E’s.
Assume independence.
a. State the three conditions of the Central Limit Theorem and explain whether each condition is satisfied in this scenario.
(9 pts.)
b. Find the mean and standard error of the Normal model for the distribution of sample proportions in this example. (5 pts.)
6. Suppose that the N(10, 3) model is a good description of the distribution of boxer puppies lengths. What is the probability
that a randomly selected boxer puppy will be between 12 and 14 inches long? Show every step or you get no credit. (10 pts.)
7. Explain the difference between a parameter and a statistic. (5 pts.).