Probability Distribution Problem Set

week4mathquestions.xlsx

Problem 1

Figure below gives the boxplots comparing the base yearly salaries of employees
in marketing and employees in research for a large company. Identify the five number summaries.
for each profession. Interpret them like we did in the class.
Marketing	Research
Min
Max
First Quartile
Second Quartile
Third Quartile
Marketing Interpretations	Research Interpretations
Interpretation of Minimum	Interpretation of Minimum
Hint: The minimum salary is xx.	Hint: The minimum salary is xx.
Interpretation of Maximum	Interpretation of Maximum
Hint: The maximum salary is xx.	Hint: The maximum salary is xx.
Interpretation of First Quartile	Interpretation of First Quartile
Hint: 25% of salaries are less than xx. 75% are greater than xx.	Hint: 25% of salaries are less than xx. 75% are greater than xx.
Interpretation of Second Quartile	Interpretation of Second Quartile
Hint: 50% of salaries are less than xx. 50% are greater than xx.	Hint: 50% of salaries are less than xx. 50% are greater than xx.
Interpretation of Third Quartile	Interpretation of Third Quartile
Hint: 75% of salaries are less than xx. 25% are greater than xx.	Hint: 75% of salaries are less than xx. 25% are greater than xx.

An insurance company determines that in every 100 claims, 4 are fraudulent.

What is the probability that the next claim the company processes will be

fraudulent?

Please state the probability as a decimal value.

A review of emergency room records at rural Millard Fellmore Memorial 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	0.2725
1	0.3543
2	0.2303
3	0.0998
4	0.0324
5	0.0084
6	0.0023
Determine the probability that the number of patients entering the emergency room
during a randomly selected 1-hour period is
a) 2 or more
b) exactly 5
c) fewer than 3
d) at most 1

Find the missing probability in the following probability distribution.
x	P(x)
0	0.07
1	0.20
2	0.38
3
4	0.13

Determine whether the distribution given below are valid probability distributions or not.
x	P(x)
0	0.30
1	0.25	(Choose one)
2	0.25
3	0.15
4	0.05

Determine whether the random variable x is discrete or continuous
a. Let x represent the number of pumps in use at a gas station	(Choose one)
b. Let x represent the weight of a truck at a weigh station	(Choose one)