180,231 views
25 votes
25 votes
An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of 580 and a standard deviation of 120. The individuals who exceed 750 on this test are considered to be potential leaders. What proportion of the population are considered to be potential leaders

User Reghunaath A A
by
2.7k points

1 Answer

17 votes
17 votes

Answer:

0.0778 = 7.78% of the population are considered to be potential leaders

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
image and standard deviation
image, the z-score of a measure X is given by:


image

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 580 and a standard deviation of 120.

This means that
image

What proportion of the population are considered to be potential leaders?

Proportion of those who exceed 750, that is, 1 subtracted by the vpalue of Z when X = 750.


image


image


image


image has a pvalue of 0.9222

1 - 0.9222 = 0.0778

0.0778 = 7.78% of the population are considered to be potential leaders

User Emily Kothe
by
3.4k points