Homework 4 – Six Problems
Note:You may use Minitab when appropriate and include the Minitab output in your homework. To place
Minitab output into your homework, highlight the portion of the Minitab printout you want, copy
that to the clipboard, and then paste it into the document
Useful learning tool: “Viewlets for Lesson 4” is posted in the “Additional Course
Resources” folder. The viewlets there show:
1. the relationship between probability and cumulative probability of binomial
distribution
2. how to use standard normal table to find probability to the left of z
3. given probability, how to find z value
4. using Minitab to find cumulative probability and probability of binomial
distribution, also using Minitab to find z-value of normal distribution
5. a viewlet for practice homework problem 5
1. Let Y be a binomial random variable with n = 12 and π = 0.3. Find the following
values (you may use Minitab):
a. P(Y ≤ 5)
b. P(Y > 5) [you should be able to get this pretty easily, without adding up lots of
numbers.]
c. P(Y > 7)
2. Demand of a certain book in a bookstore on any given day is given by the following
table (y represents the number of purchases of that book on any given day):
y
0
1
2
3
4
5
6
7
P(y)
0.1
0.23
0.31
0.12
0.1
0.05
0.05
0.04
Find:
a. the probability that on any given day the demand is more than 6.
b. The probability that on any given day the demand is less than or equal to 3.
c. On 5 randomly chosen days, what is the probability that 3 of the 5 days
have demand more than 6.
3. In an inspection of automobiles in a city, 35% of all automobiles had emissions that
did not meet EPA regulation. We take a random sample of 10 automobiles. Let X
denote the number of automobiles in the sample that fail the inspection. Construct a table
that shows the binomial probabilities and cumulative binomial probabilities. It is
similar to the last page shown in Viewlet for Lesson 4: “Binomial Probability and
Cumulative Probability” in the “Additional Course Resource” folder. [Pay attention
to the relation between P(X=x) and P(X <=x).Note that you may use Minitab to find
the probabilities, etc and then type those in to create the table.] Thus, for this
problem, the probability of failing the inspection is 0.35 and there are 10 automobiles.
Use the table to answer:
a. What is the probability that exactly 3 of the 10 failed the inspection?
b. What is the probability that 4 and more of the 10 failed the inspection?
c. What is the probability that at least 5 of the 10 failed the inspection?
4. Over a long period of time in a large multinational corporation, 15% of all sales
trainees are rated as outstanding, 75% are rated as excellent/good, 6% are rated as
satisfactory, and 4% are considered unsatisfactory. Compute the probability that 4 out of
the 10 trainees are rated as satisfactory or excellent/good.
5. Find a value for z, say z0, such that P( - z0 < Z < z0) = 0.95.
6. The College Boards, which are administered each year to many thousands of high
school students, are scored so as to yield a mean of 500 and a standard deviation of 100.
These scores are close to being normally distributed. An exclusive club wishes to invite
those scoring in the top 10% on the College Boards to join.
a. What score is required to be invited to join the club?
b. What score separates the top 75% of the population from the bottom 25%? What do
we call this value?
[hint: the score that separates the top 20% of the population from the bottom 80% is
called the 80th percentile]