1. The federal government discovered serious
contaminants in the tuna fish packed by Seaside Packing, requiring a recall of
the suspected cases of tuna. Before the
discovery was made they had produced a total of 10,000 cases of which 7,000
came from an early run and the remaining 3,000 came from a later run. It is believed that 30% of the cans in the
early run have been contaminated, and 60% of the cans in the later run have
been contaminated.
[a]
A can is chosen randomly from a case to be inspected. What is the probability that the can will be contaminated?
_______
[b]
Suppose that the can is found to be contaminated. What is the probability that it came from the early run?_____________
2. In the United States, 10% or adolescent girls have iron deficiency. Suppose twenty
adolescent girls are chosen at random.
[a] The number of girls expected to have iron
deficiency is ________, give or take ________, or so.
[b] Find the probability that exactly one of the
girls has an iron deficiency _________
[c] Find the probability that at least one of
the girls has an iron deficiency __________
[d] Find the probability that between one and
three (inclusive) have an iron deficiency. ________________
3. A study is made of the
age at entrance of college freshmen.
The SD turned out to be one of the following. Which one was it?
_______ One
month; _______ One year; _______ Five years. Explain.
4. In a certain city, tow truck operators
monitor police emergency calls so as to be the first at an accident scene. Midview Collision Co responds to accident
scenes 75% of the time. Crossland
Collision Co. responds to accident scenes only 53% of the time. Each tow company operates independently of
the other.
[a]
What is the probability that at least one of them responds to a police report
of a major accident? ____________
[b]
What is the probability that exactly one of them responds? ____________ [c] What is the probability that both
respond? ____________
[d]
What is the probability that neither respond? ____________
5. Two drugs,
zidovudine and didanosine, were tested for the effectiveness in preventing
progression of HIV disease in children.
In a double-blind clinical trial, 276 children with HIV were given
zidovudine, and 281 were given didanosine.
The following table shows the survival data for the two groups. Use the binomial
exact test at the 10% level of
significance to decide whether Didanosine is associated with a lower death rate
than Zidovudine. Use pi = .50
|
|
Died |
Survived |
Row Total |
|
Zidovudine |
15 |
259 |
274 |
|
Didanosine |
5 |
274 |
279 |
|
Column Total |
20 |
533 |
553 |
Null
Hypothesis __________________________________________ Alternative Hypothesis __________________________________________
α = ____________ Test statistic
____________________________Table from the book to use for this problem is on
page ________
P-value
=
_________________________________
Circle the correct decision:
Fail to reject the Null
Reject the Null
Detailed
conclusion:
6. The St. Louis
encephalitis virus is spread by migrating birds and mosquitoes. The probability that an infected person gets
sick is less than 1%. But of the people
who get sick, about 5% die. In a sample
of 70 independent cases of people who are sickened by encephalitis, find the
probability that at least three die.
7. The
random variable X is given by the uniform density function f(x) = ½ on the
interval (3,5) and f(x) = 0 elsewhere.
[a] Find the mean ____________ and [b] the standard
deviations _______________. [c] Find
Pr( 1 < X < 3.5) =
____________________
8. The
random variable X has the cumulative distribution function F(x) = x3,
for 0 < x < 1.
Find f(x)
= _____________ for x < 0, f(x) =
_____________ for 0 < x < 1,
f(x) = _____________ for x >
1
Find the mean ______________ and standard deviation
_______________ Find Pr(.5 < X <
2) = __________________
9. Suppose that one out of 48 chicken eggs have
fragile shells which are likely to be damaged in shipment. Also suppose that eggs are randomly packaged into cartons, each carton
containing a dozen eggs. Find the
probability that a carton containing 12 eggs has at least one such fragile egg.
10. A lot of 12 television sets includes three
that are defective. Two of the sets are shipped to a hotel.
[a] Find the probability function for the number
of defective TV's shipped to the hotel.
[b] Find the cumulative distribution function.
[c] How many defective sets can the hotel
expect?
[d] What is the variance?
11. A double blind study was performed on
consumers comparing a new formulation of a diet soft drink with the original
formulation.
Of
100 subjects, 57 preferred the new formulation, 38 preferred to original
formulation, and 5 were undecided or could not tell the
difference. Use the sign test to decide whether
consumers prefer the new formulation at the 5% level.
Null
Hypothesis __________________________________________ Alternative Hypothesis __________________________________________
α = ____________ Test statistic
____________________________Table from the book to use for this problem is on
page ________
P-value
=
_________________________________
Circle the correct decision:
Fail to reject the Null
Reject the Null
Detailed
conclusion:
1. The
prevalence of prostatic cancer in white males is 35 per 100,000,
or .00035. The sensitivity of
the radioimmunoassay for prostatic acid phosphatase (RIA-PAP) as a test for
prostatic cancer is 0.70.
Its specificity is 0.94.
[a] What
percentage of the white male population tests positive for the RIA-PAP
test? ________________
[b] If a
white male tests positive, what is the probability that he has prostatic
cancer? __________________
2. Among 16 computer disk drives in stock at a
lab, 11 are new and 5 have been rebuilt after a previous
failure. Two of the disk drives are randomly selected for a networking
experiment.
[a] Make a table
of the probability mass function for the number of disk drives selected which
are rebuilt.
[b] Find the
probability that at least one of the selected drives will be rebuilt?
___________________
[c] Find the mean
__________ and standard deviation ________ for the numbers of selected rebuilt
drives.
3. An
article in USA Today stated that “Internal surveys paid for by directory
assistance providers show that even the most accurate companies give out wrong
numbers 15% of the time.” Assume
that you are testing AT&T by making 20 requests and also assume that
this provider gives the wrong number 15% of the time.
[a] You
expect to get the wrong number ______________ times, give or take
_____________, or so.
Find the probability that among your 20 requests
[b] none are wrong numbers ______ [c] exactly one is a wrong number _______ [d] at least one is a wrong number
_____
[e]
compute the probability that at least 2 are wrong numbers
______________
4. Suppose that 15% of all service contract of a major appliance require
service. Of 1000 customers, what is the probability that fewer than 120 require service. ____________________
5. Given the probability density function f(x)
= 3x2/8 for
0 < x < 2 and 0
elsewhere,
[a] find the cumulative distribution
function
_____________________if x
< 0
F(x)
= _____________________if 0 <
x < 2
_____________________if x
> 2
[b]
P(X > 1) = __________
[c] E(X)
= __________
[d] SD(X)
= __________
in primates,
researchers divided 120 rhesus monkeys into two equal groups; over the span
of more than 10 years, one group ate without limit and the other
groups consumed only 70% as many calories as the first group. In the low-calorie group 2 monkeys developed cancer, and in the well-fed
group, 7 monkeys had cancer. Perform the binomial exact test at the 5% level to decide whether a low-calorie diet is associated with reduced
risk of cancer.
|
|
Cancer |
No Cancer |
Total |
|
Low Cal |
2 |
58 |
60 |
|
Well-Fed |
7 |
53 |
60 |
|
Total |
9 |
111 |
120 |
Null Hypothesis:
__________________________________ Alternative Hypothesis:
________________________________
Alpha = ______________ Test statistic
_________________ The table you use for this test in on page _______ of the
text.
P-Value =
__________________ Decision is
to Reject H0 Retain H0 (choose one option).
State your decision in plain English in context
of the problem____________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
7. A three-month program of physical fitness is
conducted on five subjects. The at-rest
pulse is measured before and after the program with the following results. Test whether the median at-rest pulse rate
has gone down.
Use the sign test at
the .10 level of significance
|
Subject |
1 |
2 |
3 |
4 |
5 |
|
Before |
73 |
77 |
68 |
62 |
72 |
|
After |
68 |
72 |
64 |
62 |
71 |
Null Hypothesis:
__________________________________ Alternative Hypothesis:
________________________________
Alpha = ______________ Test statistic
_________________ The table you use for this test in on page _______ of the
text.
P-Value =
__________________ Decision is
to Reject H0 Retain H0 (choose one option).
State your decision in plain English in context
of the problem____________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________