Statistical Methods for Business

33:136:385 Statistical Methods for Business Dr. Mehmet Turkoz

HW #2 Due Date is 6/13/2020 by 11pm

Blackboard Submissions

THERE ARE 5 QUESTIONS

QUESTIONS:

1. How much time do Americans living in or near cities spend waiting in traffic, and how much does waiting

in traffic cost them per year? The file “congestion.xlsx” includes this cost for 31 cities. For the time

Americans living in or near cities spend waiting in traffic and the cost of waiting in traffic per year:

a. Compute the mean, median, first quartile, and third quartile.

b. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.

c. Construct a boxplot. Are the data skewed? If so, how?

d. Compute the correlation coefficient between the time spent sitting in traffic and the cost of sitting

in traffic.

e. Based on the results of (a) through (c), what conclusions might you reach concerning the time spent

waiting in traffic and the cost of waiting in traffic.

2. A box of nine gloves contains two left-handed gloves and seven right-handed gloves.

a. If two gloves are randomly selected from the box, without replacement (the first glove is not returned

to the box after it is selected), what is the probability that both gloves selected will be right-handed?

b. If two gloves are randomly selected from the box, without replacement (the first glove is not returned

to the box after it is selected), what is the probability that there will be one right-handed glove and

one left-handed glove selected?

c. If three gloves are selected, with replacement, what is the probability that all three will be left-

handed?

d. If you were sampling with replacement, what would be the answers to (a) and (b)?

3. Olive Construction Company is determining whether it should submit a bid for a new shopping center. In

the past, Olive’s main competitor, Base Construction Company, has submitted bids 70% of the time. If Base

Construction Company does not bid on a job, the probability that Olive Construction Company will get the

job is 0.50. If Base Construction Company bids on a job, the probability that Olive Construction Company

will get the job is 0.25.

a. If Olive Construction Company gets the job, what is the probability that Base Construction Company

did not bid?

b. What is the probability that Olive Construction Company will get the job?

4. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student

has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she

will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question

and replaces the ball in the box. The marking on the ball will determine her answer to the question. There

are five multiple choice questions on the exam. What is the probability that she will get

a. Five questions correct?

b. At least four questions correct?

c. No questions correct?

d. No more than two questions correct?

33:136:385 Statistical Methods for Business Dr. Mehmet Turkoz

5. The following is a set of data from a sample of 11 items (Show your hand calculations).

X: 7 5 8 3 6 0 2 4 9 5 8

Y: 1 5 4 9 8 0 6 2 7 5 4

a. Construct a scatter plot using the sample data.

b. Calculate the mean, median variance and coefficient of variation and z-scores for X.

c. Determine the outliers.

d. Determine the quartiles of X.

e. Construct a box plot and determine the shape of X.

f. Is there a relationship between two variables X and Y? Explain.

g. What is the correlation between X and Y?

h. Approximately (Empirical Rule) how many of the data points in a bell-shaped distribution is

within 1 standard deviation of the mean.