team assignment

Wk4MeasuresofRelativeStandingandProbabilityDistributionProblemSetTemplate.xlsx

Problem 1

The box plots below compare the base yearly salaries of employees in marketing and research for a large company.
Identify the five number summaries for each profession. Interpret each in everyday language.
A. Five Number Summary	Lind et al. (2021) LO4-3 Construct and analyze a box plot
Example Interpretation
Marketing	Research	Approximate the values	Their body weight was observed as more than 99 and under 234 pounds. One-half of the subjects' weight was 149 pounds or greater. Twenty-five percent of the weight was under 125 pounds and over 169 pounds. There were no observed outliers.
Min
Max
First Quartile
Second Quartile
Third Quartile
B. Interpretations	Example
Min	99
Interpretation Marketing	Max	234
Median	149
1st Quartile	125
3rd Quartile	169
Interpretation Research

An insurance company determines that in every 100 claims, 3 are fraudulent.
What is the probability that the next claim the company processes will be
fraudulent?
Please state the probability as a decimal value.	Lind et al. (2021) LO5-2 Classical Probability
(show your calculation)

Probability Distribution	Lind et al. (2021) LO6-1 What Is a Probability Distribution?
A. A review of emergency room records at rural William Tell Hospital was performed to determine the probability
distribution of the number of patients entering the emergency room during a 1-hour period. The following table
lists this probability distribution.
Patients per hour	Probability
0.00	0.2440
1.00	0.3543
2.00	0.2001
3.00	0.0998
4.00	0.0101
5.00	0.0084
6.00	0.0833
Determine the probability that the number of patients entering the emergency room
during a randomly selected 1-hour period is
a) 2 or more	Show which values were used.
b) exactly 5	Show which values were used.
c) fewer than 3	Show which values were used.
d) at most 1	Show which values were used.
B. Determine whether the distribution given below are valid probability distributions or not.
x	P(x)
0	0.300
1	0.240	(Choose one)
2	0.250
3	0.160
4	0.050
C. Find the missing probability in the following probability distribution.
x	P(x)
0	0.070
1	0.180
2	0.220
3
4	0.130

Binomial Distribution	Lind et al. (2021) LO6-4 Binomial Probability Distribution
A recent survey by the American Accounting Association revealed 52% of accountants have the Certified Public Accounting (CPA) certificate.
Suppose we select a sample of 15 accountants.
a. What is the probability that five of the 15 accountants are CPAs?
b. What is the probability that seven or eight of the 15 accountants are CPAs?

Determine whether the random variable x is discrete or continuous	Lind et al. (2021) LO6-2 Random Variables
a. Let x represent your body height (inches)	(Choose one)
b. Let x represent the number of students in class	(Choose one)

The weekly incomes of shift foremen in the glass industry follow the normal probability distribution with a population mean of $1,500 and a population standard deviation of $100.
Lind et al. (2021) LO7-3 The Standard Normal Probability Distribution
a. What is the z value for the income of a foreman who earns x = $1,600 per week?	z =	Show your work.
b. What is the z value for the income for a foreman who earns x = $1300 per week?	z =
What is the probability associated with a., and b. above?
Look-up Lind et al. (2021) Appendix B.3 Areas under the Normal Curve	Or use the Lane Probability Calculator	Lind et al. (2021) LO7-3 Finding Areas under the Normal Curve
a.	p =
b.	p =
What is the likelihood of selecting a foreman whose weekly income is between $1300 and $1600?	p =
References
Lane, D. (n.d.). Normal distribution . http://onlinestatbook.com/2/calculators/normal_dist.html	Probability Calculator
Lind, D., Marchal, W., & Wathen, S.A. (2021). Statistical techniques in business and economics (18th ed.). McGraw-Hill.	Course Textbook

Lane Binomial Calculator	http://onlinestatbook.com/2/calculators/binomial_dist.html
Recent audit of computer chips found 15% produced in a particular factory are defective. If 25 chips are randomly selected,
a. What is the probability that none of the chips are defective?
b. What is the probability of less than 2 chips are defective?
Excel Function Method	Lane Online Calculator
=BINOM.DIST(Number,Trials.Probability,Cumulative)	Enter Data
N	25	25
a.	=BINOM.DIST(0,25,0.15,FALSE)	0.0172	π	0.15	0.15
x	0, 0	Less than 2
Explanation of a.	Calculated
FALSE is used for a single value, 0	p =	0.0172	0.0931
b.	=BINOM.DIST(1.99999,25,0.15,TRUE)	0.0931
Explanation of b.
Number 1.99999 is used to indicate less than 2
TRUE is used for multiple values, 0 to 1.99999

Lane Probability Calculator	http://onlinestatbook.com/2/calculators/normal_dist.html
Using Lind et al. (20210 Appendix B.3 is the manual means for calculating probability. It is difficult because
until the learning curve is achieved. Lane, who is a professor at Rice University, Houston, TX.,
created this web calculator, which provides a visual. Both methods will be illustrated.
Manual Method	Lane Online Calculator
µ = 100	σ = 10	x = 75	x = 110
Enter Data
z = (x - µ) / σ	z = (75-100) / 10	z = (110-100) / 10	Mean	100	100	100
z =	-2.50	1.00	SD	10	10	10
x	75, 100	Left of mean	100, 110	Right of mean	75, 110	Between
a. What is the probability :	Calculated
Appendix B.3	p	0.4938	0.3413	0.8351
z = -2.50	z	p
z = 1.0
b. What is the probability between z = -2.5 and 1.0 =	0.4938
0.3413
0.8351

Lane, D. (n.d.). Binomial distribution. http://onlinestatbook.com/2/calculators/binomial_dist.html

Lane, D. (n.d.). Normal distribution. http://onlinestatbook.com/2/calculators/normal_dist.html

Lind, D., Marchal, W., & Wathen, S.A. (2021). Statistical techniques in business and economics (18th ed.). McGraw-Hill.

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