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Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu SAMPLE MIDTERM 06
Question 1. (2 marks) A device has 2 parts with probabilities of broken of the first part
and second are 0,1; 0,2. The probability that both parts are broken is 0.04. Find probability to:
a. (1 mark) There is at least one part that works wel .
b. (0,5 marks) Only first part works wel .
c. (0,5 marks) Part 1 works wel if part 2 is broken.
Question 2. (2 marks) An automobile dealer calculates the proportion of new cars sold that
have been returned a various numbers of times for the correction of defects during the
warranty period. The results are shown in the fol owing table. Number of returns 0 1 2 3 4 Proportion 0,28 0,36 0,23 0,09 0,04
a. (1 mark) Calculate the cumulative probability distribution.
b. (0,5 marks) Find the mean of the number of returns of an automobile for corrections for
defects during the warranty period.
c. (0,5 marks) Find the variance of the number of returns of an automobile for corrections
for defects during the warranty period.
Question 3. (1 mark) A public interest group hires students to solicit donations by
telephone. After a brief training period students make cal s to potential donors and are paid
on a commission basis. Experience indicates that early on, these students tend to have only
modest success and that 70% of them give up their jobs in their first two weeks of
employment. The group hires 6 students, which can be viewed as a random sample. What
is the probability that at least 2 of the 6 wil give up in the first two weeks?
Question 4. (2 marks) Given the density function of a random variable X . fx  5(1 x) khi x (0,1) () 0 khi x (0,1)  4 
a. (1 mark) Find the probability that X is greater than 0,5. 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu b  . (1 mark) LYet X 32
. Calculate the expected value of Y .
Question 5. (2 marks) It has been found that times taken by people to complete a particular
tax form fol ow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes.
a. (1 mark) What is the probability that a randomly chosen person takes less than 85
minutes to complete this form?
b. (1 mark) Five percent of al people take more than how many minutes to complete this form?
Question 6. (1 mark) A sealed box contains 4 red cards, 4 black cards and 6 white cards.
Suppose that you wil get +1 point for each red card, -1 point for each black card, 0 point
for each white card. Now you wil toss a coin. If the outcome of the tossing is a head, you
wil randomly take 3 cards from the box. On the other hand, if the outcome of the coin flip
is a tail, 4 cards will be taken from the box at random. Find the probability that you wil
get only 1 point? If you get 1 point, what is the most likely outcome of the coin flip? 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu SAMPLE MIDTERM 07
Question 1. (2 marks) In a campus restaurant it was found that 35% of al customers order
vegetarian meals and that 50% of al customers are students. Further, 25% of al customers
who are students order vegetarian meals.
a. (1 mark) What is the probability that a randomly chosen customer both is a student and orders a vegetarian meal?
b. (0,5 marks) If a randomly chosen customer orders a vegetarian meal, what is the
probability that the customer is a student?
c. (0,5 marks) Are the events “customer orders a vegetarian meal” and “customer is a student” independent?
Question 2. (2 marks) Students in a large accounting class were asked to rate the course
by assigning a score of 1, 2, 3, 4, or 5 to the course. A higher score indicates that the students received
greater value from the course. The accompanying table shows proportions of students
rating the course in each category. Rating 1 2 3 4 5 Proportion 0.07 0.19 0.28 0.3 0.16
a. (1 mark) Determine the probability that a rating is less than 4.
b. (1 mark) Find the mean and standard deviation of the ratings.
Question 3. (1 mark) Your computer is in serious need of repair. You have estimated that
the breakdowns occur on average 3.5 times per week. Calculate the the probability that for
an entire week your computer will get 5 shutdowns.
Question 4. (2 marks) The random variable X has probability density function as fol ows: x;ifx 0 1 f x    2 ;1xif 2x    0; for al other valuesof x
a. (1 mark) Find the probability that X takes a value between 0,2 and 1,2.
b. (1 mark) Find the mean of Y where YX 2 . 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu
Question 5. (2 marks) Scores on an achievement test are known to be normal y distributed
with a mean of 420 and a standard deviation of 80.
a. (1 mark) For a randomly chosen person taking this test, what is the probability of a score between 400 and 480?
b. (1 mark) What is the minimum test score needed in order to be in the top 10% of al people taking the test?
Question 6. (1 mark) A multiple-choice test has nine questions. For each question there
are four possible answers from which to select. Two points are awarded for each correct
answer, and one point is subtracted for incorrect answers. A student who has not studied
for this test decides to choose an answer for each question at random. Find the expected
total score on the test for this student? Suppose the instructor awards three bonus points if
the students spel their name correctly. Given the probability that a student spel his name
correctly is 0,6. Calculate the probability that the total score on the test for a student is 12? 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu SAMPLE MIDTERM 08
Question 1. (2 marks) A corporation was concerned with the basic educational skil s of its
workers and decided to offer a selected group of them separate classes in reading and
practical mathematics. Of these workers, 40% signed up for the reading classes and 50%
for the practical mathematics classes. Of those signing up for the reading classes 30%
signed up for the mathematics classes.
a. (1 mark) What is the probability that a randomly selected worker signed up for both classes?
b. (0,5 marks) What is the probability that a randomly selected worker who signed up for
the mathematics classes also signed up for the reading classes?
c. (0,5 marks) What is the probability that a randomly chosen worker signed up for at least one of these two classes?
Question 2. (2 marks) Forest Green Brown, Inc., produces bags of cypress mulch. The
weight in pounds per bag varies, as indicated in the accompanying table. Weight in pounds 44 45 46 47 48 49 50 Proportion of bags 0,04 0,13 0,21 0,29 0,20 0,10 0,03
a. (1 mark) What is the probability that a randomly chosen bag wil contain more than 45
and less than 49 pounds of mulch (inclusive)?
b. (0,5 marks) Calculate the cumulative probability distribution.
c. (0,5 marks) Compute the mean of the weight per bag.
Question 3. (1 mark) Andrew Whit aker, computer center manager, reports that his
computer system experienced three component failures during the past 100 days. What is
the probability of one or more component failures in a given day?
Question 4. (2 marks) Given the probability density function of a random variable X 1  ;  0;1 x   f  xx  0; 0,1  
a. (1 mark) Find the probability that X is between 0,2 and 0,8. b. (1  mar  k Y ) X Let 32
. Determine the variance of Y . 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu
Question 5. (2 marks) Anticipated consumer demand in a restaurant for free-range steaks
next month can be modeled by a normal random variable with mean 1200 pounds and
standard deviation 100 pounds.
a. (1 mark) What is the probability that demand wil be between 1100 and 1300 pounds?
b. (1 mark) The probability is 0,10 that demand wil be more than how many pounds?
Question 6. (1 mark) The World Series of basebal is to be played by team A and team B.
The first team to win four games wins the series. Suppose that team A is the bet er team,
in the sense that the probability is 0,6 that team A wil win any specific game. Assume also
that the result of any game is independent of that of any other. What is the probability that
a seventh game wil be needed to determine the winner? What is the probability that team
B wins the series if two teams played the total of six games? 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu SAMPLE MIDTERM 09
Question 1. (2 marks) It is known that 20% of al farms in a state exceed 160 acres and
that 60% of al farms in that state are owned by persons over 50 years old. Of al farms in
the state exceeding 160 acres, 55% are owned by persons over 50 years old.
a. (1 mark) What is the probability that a randomly chosen farm in this state both exceeds
160 acres and is owned by a person over 50 years old?
b. (0,5 marks) What is the probability that a farm in this state either is bigger than 160 acres
or is owned by a person over 50 years old (or both)?
c. (0,5 marks) What is the probability that a farm in this state, owned by a person over 50 years old, exceeds 160 acres?
Question 2. (2 marks) A car salesperson estimates the fol owing probabilities for the
number of cars that she wil sel in the next week: Number of cars 0 1 2 3 4 5 Probability 0,1 0,2 0,35 0,16 0,12 0,07
a. (1 mark) Find the mean of the number of cars that wil be sold in the week.
b. (0,5 marks) Find the standard deviation of the number of cars that wil be sold in the week.
c. (0,5 marks) The salesperson receives a salary of $250 for the week, plus an additional
$300 for each car sold. Find the mean of her total salary for the week.
Question 3. (1 mark) A state senator believes that 25% of al senators on the Finance
Commit ee wil strongly support the tax proposal she wishes to advance. Suppose that this
belief is correct and that 5 senators are approached at random. What is the probability that
at least 1 of the 5 wil strongly support the proposal?
Question 4. (2 marks) Given the density function of a random variable X 3 4x  ;x 0 1 f  xx  0 ;  0;1 
a. (1 mark) Find the probability that X is less than 0,25. 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu
b. (1 mark) Determine the variance of X.
Question 5. (2 marks) The company’s sales experience indicates that daily cell phone sales
in its stores fol ow a normal distribution with a mean of 60 and a standard deviation of 15.
The marketing department conducts a number of routine analyses of sales data to monitor sales performance.
a. (1 mark) What proportion of store sales days wil have sales between 85 and 95 given
that sales are fol owing the historical experience?
b. (1 mark) Find the cutoff point for the top 10% of al daily sales.
Question 6. (1 mark) Package I has 4 products of type A, 6 products of type B. Package II
has 5 products of type A, 5 products of type B. From Package I, 2 product is randomly
selected to put into Package II. Then we randomly select 1 product from Package II. What
is the probability that the product taken from Package II is type A? Suppose that the product
taken from Package II is type B, what is the probability that the number of products of type
A taken from Package I is one? 14:07, 11/01/2026
Sample Midterm Review - Probability & Statistics Exam Preparation - Studocu