Download Practice Exam 2 - Montgomery College

Math 116 - Exam 2 - Chapters 4, 5, 6, 7
Name___________________________________
MUST SHOW WORK IN ALL PROBLEMS. REMEMBER TO SHOW SET UP OF THE PROBLEM!!
IF YOU ARE USING THE CALCULATOR INDICATE THE FEATURE USED, THE ARGUMENTS AND THE
ANSWER.
1) Privacy is a concern for many users of the Internet. One survey showed that 59% of Internet users are
somewhat concerned about the confidentiality of their e-mail. Suppose a random sample of 8 Internet users
is selected,
a) What are the possible values of the random variable x, the number of Internet users out of 8 which are
somewhat concerned about the confidentiality of their e-mail.
b) Find the probability that exactly 6 are concerned about the privacy of their e-mail.
c) Find the probability that at most 1 (one or less) are concerned about the privacy of their e-mail.
d) Based on the answer to part (c), is it unusual for one or less Internet users to be concerned about the
privacy of their e-mail? Explain why or why not.
e) Find the expected number of Internet users that are concerned about the privacy of their e-mail in groups
of 8. That is, find the mean μ of this probability distribution. Show your work here.
f) Find the standard deviation σ of the probability distribution. Show work here.
g) Use the range rule of thumb to determine usual and unusual outcomes of this experiment. Show all your
work.
List usual outcomes here _____________________________
List unusual outcomes here ____________________________
2) The lifetime of a SuperTough AAA battery is normally distributed with a mean μ = 28.5 hours and standard
deviation σ = 5.3 hours.
a) For a battery selected at random, what is the probability that the lifetime will be 30 hours or more?
SHOW ALL WORK HERE. ALSO, SHOW GRAPH, LABEL AND SHADE THE REQUIRED AREA.
NOW INDICATE HOW TO DO THE PROBLEM WITH A FEATURE IN THE CALCULATOR AND
ANSWER.
b) If we select 45 batteries at random from the mentioned population,
(i) Describe the shape, mean and standard deviation of the distribution of sample means for samples
of size 45.
shape____________________
mean .............................................
standard deviation ...................................................
(ii) What is the probability that the mean lifetime of the 45 batteries will be 30 hours or more?
SHOW ALL WORK HERE. ALSO SHOW GRAPH, LABEL AND SHADE THE REQUIRED AREA.
NOW INDICATE HOW TO DO THE PROBLEM WITH A FEATURE IN THE CALCULATOR AND
ANSWER.
c) Interpret the results from part (b).
Is it usual (common) or unusual to select a sample of 45 batteries from the above population and observe a
mean lasting life of 30 hours or more? Explain why.
Solve the problem.
3) Quality control studies for Dependable Dishwashers show the lifetime of a dishwasher follows a normal
distribution with a mean μ = 8 years and a standard deviation σ = 1.2 years. The company will replace any
dishwasher that fails during the guarantee period.
a) How long should the company's dishwashers be guaranteed if the company wishes to replace no more
than 2% of the dishwashers? (You are finding the second percentile here) (Round to the nearest tenth of a
year)
SHOW ALL WORK AND GRAPHS HERE:
The company should guarantee the dishwashers for .................................. years.
CALCULATOR WORK HERE:
b) Now USE THE CALCULATOR ONLY to find the score that separates the top 10% of the distribution.
What percentile is this? (Round to the nearest tenth of a year)
The score that separates the top ten percent of the distribution is _____________.
This score is at the ______________ percentile
4)
This is the problem in which both distributions, BINOMIAL and NORMAL come together.
We know that 54.9% of students in Montgomery College are female.
Experiment: SUPPOSE we select 15 students at random and count the number of female students
in groups of 15. Give the values for n and p in this experiment
n=
p=
a) Show that the normal approximation is appropriate to estimate the binomial distribution.
b) What are the mean and the standard deviation of this probability distribution? Show how you
find them.
c) Find the EXACT probability that the number of females in the group of 15 is exactly seven.
(Here you are using methods from chapter 5)
d) Use the normal distribution to ESTIMATE probability that the number of females in the group of
15 is exactly seven. (Here you are using the methods from chapter 6 and the continuity correction
factor). USE THE CALCULATOR ONLY. Show the feature used with corresponding numbers,
and the answer.
e) Use the normal distribution to ESTIMATE probability that we obtain LESS than or equal to 7
female students in groups of 15. (Here you are using the methods from chapter 6 and the continuity
correction factor). USE THE CALCULATOR ONLY. Show the feature used with corresponding
numbers, and the answer.
Use the given table to find the indicated probabilities. WRITE ALL ANSWERS AS DECIMALS WITH 3 OR MORE
DECIMAL PLACES
5) College students were given three choices of pizza toppings and asked to choose one favorite. The following
table shows the results.
toppings
freshman
sophomore
junior
senior
TOTALS
cheese
14
12
18
27
71
meat
26
27
12
14
79
veggie
12
14
26
27
79
TOTAL
52
53
56
68
229
If we select a student at random, what is the probability that the student selected
a) is a freshman and likes cheese topping.
b) is a sophomore or likes meat topping
c) is a senior or a junior
d) is someone who likes veggie topping.
e) is a freshmen or junior or likes veggie topping.
f) If we select two students at random, what is the probability that they are both juniors.
(I) Assume with replacement
(II) Assume without replacement
6)
According to the Federal Communications Commission, in 2002, 70% of all U.S. households had cable
television.
a) Give the shape, mean and standard deviation of the distribution of sample proportions for samples of size
300.
shape____________________ (justify answer)
mean .............................................
standard deviation ...................................................
b) USE THE NORMAL DISTRIBUTION (without the continuity correction factor) to estimate the following
probability.
What is the probability that in a sample of 300 households at least 76.7% of them have cable television?
SHOW ALL WORK HERE:
SHOW CALCULATOR FEATURE WITH NUMBERS AND ANSWER HERE: