Transcript Week 6, Lecture 1, Revision of probability and probability distributions

QBM117
Business Statistics
Probability and Probability Distributions
Revision
1
Objectives
•
To recognise the correct technique for solving
probability problems.
•
To learn how to use the probability flow chart to
assist in determining the appropriate distribution to
use when solving problems.
2
Question 1
An important part of customer service responsibilities of
a telephone company relates to the speed with which
problems in residential service can be repaired.
Suppose past data indicate that the likelihood is 0.70
that a problem in residential service can be repaired on
the same day.
1. For the first five problems reported on a given day,
what is the probability that
a. all five will be repaired on the same day?
b. at least 3 will be repaired on the same day?
c. none will be repaired on the same day?
2. For the first five problems reported on a given day
what is the expected number of problems that will be
repaired on the same day?
Question 2
Battery manufacturers compete on the basis of the
amount of time their product lasts in cameras and
toys. A manufacturer of alkaline batteries has
observed that its batteries last for an average of 26
hours when used in a toy racing car. The amount of
time is normally distributed with a standard deviation
of 2.5 hours.
1. What is the probability that a battery lasts
a. between 24 hours and 28 hours?
b. longer than 24 hours?
c. less than 20 hours?
2. What length of time will at least 90% of the
batteries last?
Question 3
A survey of top executives revealed that 35% of
them regularly read Time magazine, 20% read
Newsweek, and 10% of them read both Time and
Newsweek.
a. What is the probability that a particular top
executive reads either Time or Newsweek?
b. Given than a top executive reads Newsweek,
what is the probability that they read Time?
c. Are the events mutually exclusive? Explain.
d. Are the events independent? Explain.
e. What is the probability that a particular top
executive reads neither Time or Newsweek?
Question 4
The flight time of an airplane traveling Chicago to
New York is normally distributed from 120 minutes to
140 minutes.
a. What is the probability of a flight time of less than
125 minutes?
b. What is the probability of a flight time between
128 and 136 minutes?
c. What is the expected flight time?
Question 5
Airline passengers arrive randomly and
independently at the passenger screening facility at
Sydney International Airport. The mean arrival rate is
10 passengers per minute.
What is the probability that there are
a. no arrivals in a 1 minute period?
b. three of fewer arrivals in a 1 minute period?
c. no arrivals in a 15 second period?
d. at least one arrival in a 15 second period?
Question 6
The waiting time at a certain bank is normally
distributed with a mean of 3.7 minutes and a
standard deviation pf 1.4 minutes.
a. What is the probability that a customer has to
wait no more than 2 minutes?
b. What is the probability that a customer has to
wait between 4 and 5 minutes?
c. 20% of customers will have to wait longer than
how many minutes?
Question 7
A customer service supervisor regularly conducts a
survey of customer satisfaction. The results of their
last survey indicate that 8% of customers were not
satisfied with the service they received at their last
visit to the store. Of those who are not satisfied, only
22% return to the store within the year. Of those who
are satisfied, 64% return within the year. A customer
has just entered the store. He informs you that it is
less than 1 year since his last visit to the store. What
is the probability that he was satisfied with the service
he received on his last visit to the store?
Question 8
Large sheets of plastic are cut into smaller pieces to
be pressed into credit cards. One manufacturer uses
sheets of plastic known to have approximately 3
defects per square meter. The defects occur
randomly and independently
1. An inspector examines a randomly chosen
square meter. What is the probability of the
inspector finding
a. no defects?
b. more that 2 defects?
c. at most 3 defects?
2. What is the expected number of defects per
square meter?
Question 9
5% of a batch of invoices being audited contain
errors. A random sample of 10 invoices is taken from
the batch.
1. What is the probability that the sample contains
the following:
a. two or less invoices with errors?
b. less that two invoices with errors?
c. two or more invoices with errors?
d. more than two invoices with errors?
e. exactly two invoices with errors?
2. What is the expected number of invoices with
errors?
Question 10
Psychologists believe that there is a relationship
between aggressiveness and order of birth. To test
this belief, a psychologist chose 500 primary school
students at random and administered each student to
a test designed to measure aggressiveness. Each
student was classified into one of four categories.
The results are shown in the table below.
First born Not first born
Aggressive
75
Not Aggressive 125
75
225
If a student is chosen at random from the 500
a. what is the probability that the student is first
born?
b. what is the probability that the student is
aggressive?
c. what is the probability that the student is
aggressive given that the student was first born?
d. Is the event that a student is aggressive
independent of the event that the student is first
born?
Reading for next lecture
• Chapters 6 and 7
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