Statistics Through Applications
Statistics Through Applications
2nd Edition
ISBN: 9781429219747
Author: Daren S. Starnes, David Moore, Dan Yates
Publisher: Macmillan Higher Education
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Chapter 3.2, Problem 3.23E
To determine

To calculate the proportion of the data that falls above than 144 and also explain whether I is surprising or not that none of 74 students have got that high score.

Expert Solution & Answer
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Answer to Problem 3.23E

0.15% of the values fall above than 144.

Explanation of Solution

Given:

Mean = 111

Standard deviation = 11

  Statistics Through Applications, Chapter 3.2, Problem 3.23E

Concept used:

As per empirical rule

  1. 68% of the data falls within one standard deviation from the mean.
  2. 95% of the data falls within two standard deviations from the mean.
  3. 99.7% of the data falls within three standard deviations from the mean.

Calculation:

144 is three standard deviationsabove than mean, the proportion that falls above than 144 is 0.15% Therefore, approximate 0.15% of the values fall above than 144.

It’s not surprising that none of 74 students have scored that high because the probability to have that high score is less than 5% which means that it is an unusual event. So, definitely it is not a surprising event.

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