
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 13.
Question content area bottom
Part 1
a) Choose the model for these IQ scores that correctly shows what the 68-95-99.7 rule predicts about the scores.
A.
font size decreased by 3 100font size decreased by 2 mu plus sigmafont size decreased by 2 mu plus 2 sigmafont size decreased by 2 mu plus 3 sigmafont size decreased by 2 mu minus sigmafont size decreased by 2 mu minus 2 sigmafont size decreased by 2 mu minus 3 sigmafont size decreased by 2 mufont size decreased by 3 113font size decreased by 3 87font size decreased by 3 126font size decreased by 3 74font size decreased by 3 61font size decreased by 3 139
68%
95%
99.7%
A bell-shaped curve with horizontal axis from less than 61 to 139 plus in intervals of 13 begins close to the horizontal axis, increases at an increasing and then decreasing rate to its maximum at 100, labeled "mu," and decreases at an increasing and then decreasing rate approaching the horizontal axis. The curve is symmetric. The area below the curve is subdivided into regions by the intervals as follows: the region from mu minus sigma, 87, to mu plus sigma, 113, is labeled "99.7%"; the region from mu minus 2 times sigma, 74, to mu plus 2 times sigma, 126, is labeled "95%"; the region from mu minus 3 times sigma, 61, to mu plus 3 times sigma, 139, is labeled "68%."
B.
font size decreased by 3 113font size decreased by 2 mu plus sigmafont size decreased by 2 mu plus 2 sigmafont size decreased by 2 mu plus 3 sigmafont size decreased by 2 mu minus sigmafont size decreased by 2 mu minus 2 sigmafont size decreased by 2 mu minus 3 sigmafont size decreased by 2 mufont size decreased by 3 126font size decreased by 3 100font size decreased by 3 139font size decreased by 3 87font size decreased by 3 74font size decreased by 3 152
68%
95%
99.7%
A bell-shaped curve with horizontal axis from less than 74 to 152 plus in intervals of 13 begins close to the horizontal axis, increases at an increasing and then decreasing rate to its maximum at 113, labeled "mu," and decreases at an increasing and then decreasing rate approaching the horizontal axis. The curve is symmetric. The area below the curve is subdivided into regions by the intervals as follows: the region from mu minus sigma, 100, to mu plus sigma, 126, is labeled "68%"; the region from mu minus 2 times sigma, 87, to mu plus 2 times sigma, 139, is labeled "95%"; the region from mu minus 3 times sigma, 74, to mu plus 3 times sigma, 152, is labeled "99.7%."
C.
font size decreased by 3 100font size decreased by 2 mu plus sigmafont size decreased by 2 mu plus 2 sigmafont size decreased by 2 mu plus 3 sigmafont size decreased by 2 mu minus sigmafont size decreased by 2 mu minus 2 sigmafont size decreased by 2 mu minus 3 sigmafont size decreased by 2 mufont size decreased by 3 113font size decreased by 3 87font size decreased by 3 126font size decreased by 3 74font size decreased by 3 61font size decreased by 3 139
68%
95%
99.7%
A bell-shaped curve with horizontal axis from less than 61 to 139 plus in intervals of 13 begins close to the horizontal axis, increases at an increasing and then decreasing rate to its maximum at 100, labeled "mu," and decreases at an increasing and then decreasing rate approaching the horizontal axis. The curve is symmetric. The area below the curve is subdivided into regions by the intervals as follows: the region from mu minus sigma, 87, to mu plus sigma, 113, is labeled "68%"; the region from mu minus 2 times sigma, 74, to mu plus 2 times sigma, 126, is labeled "95%"; the region from mu minus 3 times sigma, 61, to mu plus 3 times sigma, 139, is labeled "99.7%."
Your answer is correct.
Part 2
b) In what interval would you expect the central 95% of the IQ scores to be found?
Using the 68-95-99.7 rule, the central 95% of the IQ scores are between
74 and
126.
(Type integers or decimals. Do not round.)
Part 3
c) About what percent of people should have IQ scores above 139?
Using the 68-95-99.7 rule, about
0.15% of people should have IQ scores above 139.
(Type an integer or a decimal. Do not round.)
Part 4
d) About what percent of people should have IQ scores between 87 and 100?
Using the 68-95-99.7 rule, about
34% of people should have IQ scores between 87 and 100.
(Type an integer or a decimal. Do not round.)
Part 5
e) About what percent of people should have IQ scores above 113?
Using the 68-95-99.7 rule, about
enter your response here% of people should have IQ scores above 113.
(Type an integer or a decimal. Do not round.)
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