WS 25 – Random Variable Name:
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(For questions 1-11) Show work and explanations on a separate piece of paper and/ or make
appropriate spacing. (12 -15 can be written in appropriate spaces.) If you can’t briefly answer the
question this implies that you do not fully understand the vocabulary and/or symbols in this section. Go
back and review, so you can discuss this material. Make sure you show all steps and use correct
translation and function notation. Attach this sheet to the top of your work
Some of this work should or can be done in excel, if you use excel attach you excel work.
1. [Hint: use excel ] ]The personnel director of a large company has several similar positions to fill. It
is estimated that there is a 55% chance that an applicant will accept a job offer that the company
makes. Suppose that all of those receiving offers make independent decisions about whether or not to
accept. Thus, the number, A, of acceptances received from n offers is a binomial random variable.
a) If 15 job offers are made, and A is the number of acceptances received from 15 offers, find the
distribution of A (this means find all possible values of A and their corresponding probabilities.
Write the f
A
(a) and F
A
(a))
b) Graph the p.m.f. of A and the c.d.f. of A. (you should do this in excel)
Attach your excel worksheet.
c) What is the probability that 6 offers will be accepted?
d) What is the probability that at least 6 offers are accepted?
2. According to a Tobacco Research and Intervention Program, only 7% of the nation’s cigarette
smokers ever enter into a treatment program to help them quit smoking. In a random sample of 25
smokers, let X be the number of smokers who enter into a treatment program.
(Write values if need to 6 decimal places or in correct scientific notation) - (attach your excel work)
a. How many smokers from this sample do you expect to enter a treatment program?
(Hint: What is the distribution of X ?)
b. Write the pdf and cdf for this distribution (hint you can use excel)
c. What is the probability that 6 smokers from the random sample will enter into a treatment program?
d. What is the probability that at most 3 smokers from the random sample will enter into the treatment
program?
e. What is the probability that at least 7 smokers from the random sample will enter into the treatment
program?
f. What is the probability that more than 2 smoker from the random sample will enter into the treatment
program?
g. What is the probability that at least 2 smoker from the random sample will enter into the treatment
program?
3. Alfred E. Neuman has three pennies, four nickels, two dimes, and one quarter in his pocket. Let X be
the denomination of a coin selected at random from his pocket.
Example: P(X=5) = 4/10 The probability that a randomly picked coin is a nickel is 40%
P(X≤ 5) =7/10 The probability that a randomly picked coin has value of a nickel or less is 70%
a) Construct a table of the p.m.f.
b) Graph the p.m.f. (either by hand or excel your choice)
c) Construct a table representing the c.d.f.
d) Write the c.d.f. as a piecewise function
e) Graph the c.d.f. (either by hand or excel your choice)
f) Find
( 10)
P X
=
g) Find
( 25)
P X
≤
h) Find
( 10)
P X
≤
i) Find
( 10)
P X
<
j) Find
( )
E X
