Stat Worksheet Alpha PDF

Statistics for business (Page 1 of 2) July 7, 2022
ALPHA UNIVERSITY COLLEGE

STATISTICS FOR BUSINESS
WORKSHEET
1. Find the number of ways a chairman, a vice-chairman, a secretary, and a treasurer can be chosen
from a committee of eight members.
2. In how many ways can a committee consisting of 2 faculty members and 3 students be formed
if 6 faculty members and 10 students are eligible to serve on the committee?
3. A company is creating three new divisions and 7 managers are eligible to be appointed head of
division. How many different ways could the three new heads is appointed?
4. Three fair coins are tossed. What is the probability of getting at most to heads?
5. Two dice are rolled simultaneously. What is the probability of getting two numbers whose
(a) sum is 9? (b) product is odd? (c) product is even?
6. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the
probability that none of the balls drawn is blue?
7. A committee of size 5 is to be selected from a group of 6 men and 9 women. If the selection is
made randomly, what is the probability that the committee consists of 3 men and 2 women?
8. A lot consists of 20 defective and 80 non-defective items from which two items are chosen without
replacement. Let events A and B are defined as
A = {the first item chosen is defective}, B = {the second item chosen is defective}
(a) What is the probability that both items are defective?

(b) What is the probability that the second item is defective?
9. If an automatic teller machine gives service for 3 customers on average in an hour then, find the
probability that 4 customers will be served in the next hour.
10. A box contains 3 defective units and 17 non-defective units. Two units are selected from the
box without replacement. What is the probability that the first defective and the second non
defective?
11. Suppose E and F are events of a sample space S for which

P (E) = 0.7 P (F ) = 0.8 P (E ∩ F ) = 0.6. Find
(a) P (E ∪ F ) (b) P (E|F ) (c) P (F |E) (d) P (Ē|F̄ )
12. If P (A) = 0.24, and P (B) = 0.52, and A and B are independent. Find P (A ∪ B).
13. Let A and B be two events of the sample space with P (A/B) = 0.3, P (B/A) = 0.6, and
P (A ∩ B) = 0.3 then find
(a) P (A) (b) P (B)
14. According to a recent study conducted by businessmen, 76% of all shareholders have some
college education. Suppose that 37% of all adults have some college education and that 22% of
all adults are share holders. For a randomly selected adult:
(a) What is the probability that the person did not own shares of stock?
(b) What is the probability that the person owns shares of stock or had some college education?
(c) What is the probability that the person has neither some college education nor owns shares
of stock?
Statistics for business (Page 2 of 2) July 7, 2022
(d) What is the probability that the person does not own shares of stock or has no college
education?
(e) What is the probability that the person owns only shares of stock or had some college
education but not both?
15. The following table is based on observing a random sample of individuals who entered in to a
gift articles shop at the center of a town
Sex Result of list Total

Purchase Not purchase
Male 40 40 80
Female 40 80 120
Total 80 120 200
(a) What is the probability that a randomly selected individual is female?

(b) What is the probability that a purchase was made given that a randomly selected individual
is female?
(c) What is the probability that a randomly selected individual is female or one who made a
purchase?
16. Motors, Inc., has two plants to manufacture cars. Plant I manufactures 80% of the cars and
plant II manufactures 20%. At plant I, 85 out of every 100 cars are rated standard quality or
better. At plant II, only 65 out of every 100 cars are rated standard quality or better.
(a) What is the probability that a customer obtains a standard quality car if he buys a car
from Motors, Inc.?
(b) What is the probability that the car came from plant I if it is known that the car is of
standard quality?
17. A variable is normally distributed with mean 6 and standard deviation 2. Find the percentage
of all possible values of the variable that
(a) lie between 1 and 7.

(b) exceed 5.
18. For some positive value of x, the probability that a standard normal variable is between 0 and
+2x is 0.1255. Find the value of x.
19. For some value of z, the probability that a standard normal variable below z is 0.3015. Find
the corresponding value of z?
20. A TV show reported that children between the ages of 2 and 5 watch an average of 25 hours of
television per week. Assume the variable is normally distributed and the standard deviation is
3 hours. If 20 children between the ages of 2 and 5 are randomly selected, find the probability
that the mean of the number of hours they watch television will be greater than 26.3 hours.
21. The average number of pounds of meat that a person consumes per year is 218.4 pounds. Assume
that the standard deviation is 25 pounds and the distribution is approximately normal.
(a) Find the probability that a person selected at random consumes less than 224 pounds per
year.
(b) If a sample of 40 individuals is selected, find the probability that the mean of the sample
will be less than 224 pounds per year.

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Statistics for business (Page 1 of 2) July 7, 2022

ALPHA UNIVERSITY COLLEGE

(a) What is the probability that both items are defective?

11. Suppose E and F are events of a sample space S for which

(a) P (E ∪ F ) (b) P (E|F ) (c) P (F |E) (d) P (Ē|F̄ )

Sex Result of list Total

(a) What is the probability that a randomly selected individual is female?

(a) lie between 1 and 7.

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