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5.11 Scores on the Wechsler Adult Intelligence Scale (WAIS) approximate a
normal curve with a mean of 100 and a standard deviation of 15. What
proportion of IQ scores are
F i n d i n g Scores
5.13 IQ scores on the WAIS test approximate a normal curve with a mean of
100 and a standard deviation of 15. What IQ score is identified with
line perpendicular to the mean (or the 50th percentile), with half of 95
percent, or 47.5 percent, above this line and the remaining 47.5 percent
below this line.]
number of hours of physical discomfort caused by their most recent colds.
Assume that their estimates approximate a normal curve with a mean of
83 hours and a standard deviation of 20 hours.
48 hours?
either above or below the mean?
and 72 hours?
[See the comment about “middle 95 percent” in Question 5.13(d) .]
the most. She will work only with those who estimate that they suffered
for more than hours.
those who suffered most. If each group is to consist of only the extreme 3
percent, the mild group will consist of those who suffered for fewer than
hours, and the severe group will consist of those who suffered for
more than hours.
C suffered, on the average, for 61 hours. What proportion of the original
survey (with a mean of 83 hours and a standard deviation of 20 hours)
suffered for more than 61 hours?
(Be careful!)
Answers on page 505 .
weight (in pounds) by the square of height (in inches) and then multiplying
by a factor of 703. A BMI less than 18.5 is defined as underweight; between
18.5 to 24.9 is normal; between 25 and 29.9 is overweight; and 30 or more
is obese. It is well-established that Americans have become heavier during
the last half century. Assume that the positively skewed distribution of BMIs
for adult American males has a mean of 28 with a standard deviation of 4.
BMI score of 28?
Key Equations
ADDITION RULE
Pr(A or B) = Pr(A) + Pr(B)
MULTIPLICATION RULE
Pr(A and B) = [Pr(A)][Pr(B)]
REVIEW QUESTIONS
about a televised event. Following a televised debate between Barack
Obama and Mitt Romney in the 2012 U.S. presidential election campaign,
a TV station conducted a telephone poll to determine the “winner.” Callers
were given two phone numbers, one for Obama and the other for Romney,
to register their opinions automatically.
*8.14 The probability of a boy being born equals .50, or 1 / 2 , as does the probability
of a girl being born. For a randomly selected family with two
children, what’s the probability of
addition or multiplication rule, satisfy yourself that the various events
are either mutually exclusive or independent, respectively.)
Answers on page 509.
8.19 A sensor is used to monitor the performance of a nuclear reactor. The
sensor accurately reflects the state of the reactor with a probability of .97.
But with a probability of .02, it gives a false alarm (by reporting excessive
radiation even though the reactor is performing normally), and with a
probability of .01, it misses excessive radiation (by failing to report excessive
radiation even though the reactor is performing abnormally).
either a false alarm or a miss?
a second completely independent sensor, and the reactor is shut
down only when both sensors report excessive radiation. (According to
this perspective, solitary reports of excessive radiation should be viewed
as false alarms and ignored, since both sensors provide accurate information
much of the time.) What is the new probability that the reactor
will be shut down because of simultaneous false alarms by both the first
and second sensors?
someone who lives near the nuclear reactor proposes an entirely
different strategy: Shut down the reactor whenever either sensor
reports excessive radiation. (According to this point of view, even a
solitary report of excessive radiation should trigger a shutdown,
since a failure to detect excessive radiation is potentially catastrophic.)
If this policy were adopted, what is the new probability
that excessive radiation will be missed simultaneously by both the
first and second sensors?
*8.21 Assume that the probability of breast cancer equals .01 for women in
the 50–59 age group. Furthermore, if a women does have breast cancer,
the probability of a true positive mammogram (correct detection of
breast cancer) equals .80 and the probability of a false negative mammogram
(a miss) equals .20. On the other hand, if a women does not
have breast cancer, the probability of a true negative mammogram (correct
nondetection) equals .90 and the probability of a false positive
mammogram (a false alarm) equals .10. (Hint: Use a frequency analysis
to answer questions. To facilitate checking your answers with those in
the book, begin with a total of 1,000 women, then branch into the number
of women who do or do not have breast cancer, and finally, under
each of these numbers, branch into the number of women with positive
and negative mammograms.)
positive mammogram?
mammogram?
Answers on page 509.
5.15 (a) 83 1 (–1.64)(20) 5 50.2
or 83 1 (–1.65)(20) 5 50
(b) .9599
(c) .1357
(d) 83 1 162.332 1202 5 e
129.6
36.4
(e) .2896
(f) 83 1 161.962 1202 5 e
122.2
43.8
(g) .7021
(h) 83 1 (0.84)(20) 5 99.8
(i) 83 1 161.882 1202 5 e
120.6
45.4
(j) .8643
(k) 0 since exactly 61 equals 61.000 etc. to infinity, a point along the base of the
normal curve that is associated with no area under the normal curve.
(b) 20.75
(c) 0.50
8.14 (a) A1–2 B A1–2 B 5 1–4
(b) A1–2) A1–2 B 5 1–4
(c) A1–4)1A1–4 B 5 2–4
8.21
1,000
Women
990
No Breast Cancer
.99
.90 .10 .20 .80
.01
891
True
Negative
99
False
Positive
10
Breast Cancer
2
False
Negative
8
True
Positive
(a)
99 1 8
1,000 5
107
1,000 5 .107
(b)
8
99 1 8 5
8
107 5 .075 .
(c)
891
891 1 2 5 .998
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