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
(a) above Kristen’s 125?
(b) below 82?
(c) within 9 points of the mean?
(d) more than 40 points from the mean?
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 wit
(a) the upper 2 percent, that is, 2 percent to the right (and 98 percent to the left)?
(b) the lower 10 percent?
(c) the upper 60 percent?
(d) the middle 95 percent? [Remember, the middle 95 percent straddles the 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.]
(e) the middle 99 percent?
8.10
Television stations sometimes solicit feedback volunteered by viewers about a tele-vised event. Following a televised debate between Barack Obama and Mitt Romney in the 2012 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.
(a) Comment on whether or not this was a random sample.
(b) How might this poll have been improved?
8.16
A traditional test for extrasensory perception (ESP) involves a set of playing cards, each of which shows a different symbol (circle, square, cross, star, or wavy lines). If C represents a correct guess and I an incorrect guess, what is the probability of
(a) C?
(b) CI (in that order) for two guesses?
(c) CCC for three guesses?
(d) III for three guesses?
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).
(a) What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?
(b) To reduce costly shutdowns caused by false alarms, management introduces 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?
(c) Being more concerned about failures to detect excessive radiation, 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
Sample Solution
