Business Statistics

Business Statistics

Homework 2 Questions. ( from the 11th edition of the book)
Chapter 3: 19, 29, 63
Question 19: The Los Angeles Times reported the air quality index for various areas of southern California. A
sample of air quality index values for Pomona provided the following data: 28,42,58,48,45,50, 60,49,50
A) Compute the range and interquartile range
B) Compute the sample variance and sample standard deviation
C) Sample of air quality index for Anaheim provided a sample mean of 48.5, a sample variance of 136 and a sample
standard deviation of 11.66. What comparison can you make between the air quality in Pomona and Anaheim on
the bases of these descriptive statistics.
Question 29: The results of a national survey showed that on average adults sleep 6.9hrs per night. Suppose that
the standard deviation is 1.2 hrs
A) Chebyshev’s Theorem to calculate the percentage of individuals who sleep between 4.5 hr to 9.3 hrs
B) Use Chebyshev’s Theorem to calculate the percentage of individuals who sleep between 3.9 hrs and 9.9. hrs
C) Assume that the number of hours of sleep follows a bell shaped distribution, use the empirical rule to calculate
the percentage of individuals who sleep between 4.5 hrs and 9.3 hrs per day. How does this result compare to
the value that you obtained using Chebyshev’s Theorem in part A
Question 63: Public Transport and the automobile are two methods an employee can use to get to work each day.
Samples of times recorded for each method are shown. Times are in minutes.
Public: 28 29 32 37 33 25 29 32 41 34
Automobile: 29 31 33 32 34 30 31 32 35 33
A) Compute the sample mean time to get to work for each method
B) Compute the sample standard deviation for each method
C) On the basis of your results form Part A and Part B, which method of transportation should be preferred ?
explain.
D) Develop a box plot for each method. Does a comparison of the box plots support your conclusion in Part C?
Page 2 of 4 Homework 2
Chapter 4: 4,18,23,32
4. Consider the experiment of tossing a coin three times.
a. Develop a tree diagram for the experiment.
b. List the experimental outcomes
c. What is the probability for each experimental outcome?
18. To investigate how often families eat at home, Harris Interactive surveyed 496 adults living with children
under the age of 18(USA Today, January 3,2007). The survey results are shown in the following table.
Number of Number of
Family Meals Survey
per week Responses
0 11
1 11
2 30
3 36
4 36
5 119
6 114
7 or more 139
For a randomly selected family with children under the age of 18,compute the following.
a. The probability the family eats no meals at home during the week.
b. The probability the family eats at least four meals at home during the week.
c. The probability the family eats two or fewer meals at home during the week.
Page 3 of 4 Homework 2
32.The automobile industry sold 657,000 vehicles in the United States during January 2009( The Wall Street
Journal ,February 4,2009). This volume was down 37% from January 2008 as economic continue to decline.
The Big Three US automakers-General Motors, Ford, and Chrysler-sold 280,500 vehicles , down 48% from
January 2008. A summary of sales by automobile manufacturer and type of vehicle sold is shown in the
following table. Data are in thousands of vehicles. The non-US manufacturers are led by Toyoa, Honda,and
Nissan. The category Light Truck includes pickup,minivan,SUV, and crossover models.
Manufacturer
Type of Vehicle
Car Light Truck
US 87.4 193.1
Non US 228.5 148.0
a. Develop a joint probability table for these data and use the table to answer the remaining questions
b. What are the marginal probabilities? What do they tell you about the probabilities associated with the
manufacturer and the type of vehicle sold?
c. If a vehicle was manufactured by one of the US automakers, what is the probability that the vehicle was a
car?
d. If a vehicle was not manufactured by one of the US automakers , what is the probability that the vehicle was
a car? What is the probability it was a light truck?
e. If the vehicle was a light truck, what is the probability that it was manufactured by one of the US automakers?
f. What does the probability information tell you about sales?
Page 4 of 4 Homework 2
Chapter 5: 9,15,31,44
Question 9: Nationally, 38% of fourth graders cannot read an age-appropriate book. The following Data show the
number of children, by age, identified as learning disability under special education. Most of these children have
reading problems that should be identified and corrected before third grade. Current federal law prohibits most
children from receiving extra help from special education programs until they fall behind by approximately two years’
worth of learning, and that typically means third grade or later ( USA Today , September 6,2001)
Age Number of Children
6 37,369
7 87,436
8 160,840
9 239,719
10 286,719
11 306,533
12 310,787
13 302,604
14 289,168
Suppose that we want to select a sample of children identified as learning disabled under special education for a
program designed to improve reading ability. Let x be a random variable indicating the age of one randomly selected
child.
A) Use the data to develop a probability distribution for x. Specify the values for the random variable and the
corresponding values for the probability function f(x).
B) Draw a graph of the probability distribution
C) Show that the probability distribution satisfies the equations (5.1) and (5.2)
Question 15: The following table provides a probability distribution for the random variable x.
x f(x)
3 .25
6 .50
9 .25
A) Compute E(x), the expected value of x.
B) Compute s2, The variance of x.
C) Compute s, the standard deviation of x.
Question 31: Nine percent of undergraduate students carry credit card balances greater then $7000 (Reader’s digest, July
2002). Suppose 10 undergraduate students are selected randomly to be interviewed about the credit card usage.
A) Is the selection of 10 students a binomial experiment? Explain.
B) What is the Probability that two of the students will have a credit card balance greater then $7000?
C) What is the Probability that none of the students will have a credit card balance greater then $7000?
D) What is the Probability that at least three will have a credit card balance greater then $7000?
Question 44: An average of 15 aircrafts accidents occur each year ( The World Almanac and Book of Facts, 2004).
A) Compute the mean number of aircrafts accidents per month
B) Compute the probability of no accidents during a month
C) Compute the probability of exactly one accident during a month
D) Compute the probability of more then one accidents during a month.
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