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Unformatted text preview: BUS152 Statistics for Social Sciences
Homework 2 – Study Set
Questions and Solutions
Questions:
Q1. When a customer places an order with Jane’s On Line Office Supplies, a computerized
accounting information system (AIS) automatically checks to see if the customer has exceeded
his or her credit limit. Past records indicate that the probability of customers exceeding their
credit limit is 0.05. Suppose that, on a given day, 20 custome rs place orders. Assume that the
number of customers that the AIS detects as having exceeded their credit limit is distributed as a
binomial random variable.
a. What are the mean and standard deviation of the number of customers exceeding their
credit limits?
b. What is the probability that 0 customers will exceed their limits?
c. What is the probability that 1 customer will exceed his or her limit?
d. What is the probability that 2 or more customers will exceed their limits?
Q2. The Melbourne Department of Transportation maintains statistics for mishandled bags per
1,000 airline passengers. In 2005, Air One had 7.09 mishandled bags per 1,000 passengers.
What is the probability that in the next 1,000 passengers, Air One will have
a. no mishandled bags?
b. at least one mishandled bag?
c. at least two mishandled bags?
Q3. The dean of a law school wishes to form an executive committee of 8 from among the 36
tenured faculty members at the school. The selection is to be random, and at the scho ol there
are 10 tenured faculty members in accounting.
a. What is the probability that the committee will contain none of faculty members in
accounting?
b. What is the probability that the committee will contain at least 2 of faculty members in
accounting?
c. What is the probability that the committee will contain no more than 2 of faculty
members in accounting? Q4. The mean download time for METU NCC Web site is 2.5 seconds. Suppose that the
download time is normally distributed with a standard deviation of 0. 5 second. What is the
probability that a download time is
a. less than 1 second?
b. between 0.5 and 1.5 seconds?
c. above 0.5 second.
1 d. 99% of the download times are above how many seconds?
Q5. A study of the time spent shopping in a supermarket in Singapore for a market basket of 40
specific items showed an approximately uniform distribution between 30 minutes and 50
minutes. What is the probability that shopping time will be
a. between 35 and 40 minutes?
b. less than 45 minutes?
c. What are the mean and standard deviation of the shopping time?
Q6. The time between unplanned shutdowns of a power plant in Paris has an exponential
distribution with a mean of 17 days. Find the probability that the time b etween two unplanned
shutdowns is
a. less than 12 days.
b. more than 18 days.
c. less than 6 days. Solutions:
Q1. Binomial Distribution
and
a. b. ( )(
Mean =
Standard deviation = ) ,
( √ ) ( √ )( ) Let X be the number of customers exceeding their credit limits
P(X = 0 ) = ?
( ) ( ( ) ) ( In Excel, = BINOMDIST(0, 20, 0.05, FALSE) yields (
c. ) ( ) ) P(X = 1 ) = ?
( ) ( ( ) ) ( ) In Excel, = BINOMDIST(1, 20, 0.05, FALSE) yields (
d. ( ) ( ) )
( ) ( ) ( ) In Excel, = 1 BINOMDIST(1, 20, 0.05, TRUE) yields ( 2 ) ( ) Q2. Poisson Distribution. Let X be the number of mishandled bags
number of mishandled bags per passenger
a.
( ( ) ) ( ) In Excel, = POISSON(0,0.00709,FALSE) yields ( ) b.
( ) ( ) ( ) In Excel, = 1 POISSON(0,0.00709,TRUE) yields (
c. ( ) )
( ) ( ) ( (
( )( ) ) ( ) ( ( ) ) ( ) ( ) )
( ) In Excel, = 1 POISSON(1,0.00709,TRUE) yields ( ) Q3. Hypergeometric Distribution () ( )( ) () N: Total number of tenured faculty members, N = 36
A: Number of tenured faculty members in accounting, A = 10
n: Number of faculty members in the committee, n = 8
X: Number of tenured faculty members in accounting that are selected for the committee
a. ( ) ( ) ( )(
( )
) In Excel, = HYPERGEOMDIST(1,8,10,36,FALSE) yields ( b. ( ) )
( ) ( ) 3 ( ) ( ) ( ( ( ( ) ) ) )( ) ( ) ( )
( In Excel, = 1 – HYPERGEOMDIST(1,8,10,36,TRUE) yields
c. ( ) ( ) ( ( ) In Excel, = HYPERGEOMDIST(2,8,10,36,TRUE) yields ( ) (
( ) ( ) ( ) ( ) ( )(
( ) ) ) ( )
)
) Q4. Normal Distribution
seconds and seconds Let X be the download time for METU NCC Web site
a. ( ) (
)
(
)
from Table E.2, p.812 (Cumulative Standardized Normal
Distribution Table posted on METUOnline, Lecture Notes)
b. ( )
( ) ( ( ) (
(
c. ( d. ( ) ( ) ) ( ) )
( ) ( ) ( ) ,x=?
( ) (
( 4 )
) )
) ( ) 0.01 corresponds to Z = – 2.33 (from Table E.2, p.812)
( )( ) seconds Q5. Uniform Distribution a = 30 and b = 50
Let X be the time spent shopping in a supermarket in Singapore
a. ( b. ( )
) c. and √ Q6. Exponential Distribution.
Let X be the time between unplanned shutdowns of a power plant in Paris
mean number of unplanned shutdowns per day
a. ( )
( ( ) )( ) In Excel, = EXPONDIST(12,1/17,TRUE) yields ( b. ( ) )
( ) ( ) )( ( ( In Excel, = 1 – EXPONDIST(18,1/17,TRUE) yields (
c. ( ( ) In Excel, = EXPONDIST(6,1/17,TRUE) yields ( 5 )
) )
( ) )( ) ) ( )( ) ...
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