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.

Answer to Problem 3.23E

0.15% of the values fall above than 144.

Explanation of Solution

Given:

Mean = 111

Standard deviation = 11

  

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.