
Concept explainers
a)
To draw the model which shows 68-95-99.7
a)

Explanation of Solution
Given:
Following is the model which shows 68-95-99.7:
b)
To find the interval in which central 95% of IQ scores to be found.
b)

Answer to Problem 26E
The interval in which central 95% of IQ scores to be found between 68 and 132
Explanation of Solution
Given:
According to rule of 68-95-99.7, the 95% of the values are within 2 standard deviation of the
Therefore,
Hence, interval in which central 95% of IQ scores to be found between 68 and 132
c)
To find the percent of people having IQ score above 116.
c)

Answer to Problem 26E
The 16% percent of people having IQ score above 116.
Explanation of Solution
Given:
According to rule of 68-95-99.7,
That means, 116 is one standard deviation above the mean. We know that 68% of the IQ scores are within 1 standard deviation of the mean. That is, 100-68 = 32% of the IQ scores are more than 1 standard deviation from the mean.
We know, the normal curve is symmetric about the mean then 16% is more than 1 standard deviation below the mean and 16% is more than 1 standard deviation above the mean.
Hence, approximately 16% of all people should have an IQ score above 116.
d)
To find the percent of people having IQ score between 68 and 84
d)

Answer to Problem 26E
The 13.5% percent of people having IQ score between 68 and 84.
Explanation of Solution
Given:
According to rule of 68-95-99.7,
That means, 116 is one standard deviation above the mean.
That means, 68 is two standard deviation below the mean.
Therefore, 95%-68% = 27% which is more than 1 standard deviation and less than 2 standard deviation of the mean. We know, the normal curve is symmetric about the mean then 13.5% is more than 1 standard deviation but less than 2 standard deviation below the mean and 13.5% is more than 1 standard deviation but less than 2 standard deviation above the mean. So, we can say, 13.5% of people having IQ score between 68 and 84.
e)
To find the percent of people having IQ score above 132
e)

Answer to Problem 26E
The 13.5% percent of people having IQ score above 132
Explanation of Solution
Given:
According to rule, 95% of the data lies between 2 standard deviations from the mean. Since, total data is 100%, so 5% of the data is the more than 2 standard deviations from the mean. Therefore, as per symmetry, 2.5% is more than 2 standard deviations below the mean and 2.5% is more than 2 standard deviations above the mean.
That means, 132 is two standard deviation above the mean.
Therefore, approximately 2.5% of people having IQ score above 132
Chapter 6 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
Basic Business Statistics, Student Value Edition
Thinking Mathematically (6th Edition)
Elementary Statistics: Picturing the World (7th Edition)
A First Course in Probability (10th Edition)
Elementary Statistics (13th Edition)
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