Respuesta :
Answer:
0.0778 = 7.78% of the population are considered to be potential leaders
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]\mu = 580, \sigma = 120[/tex]
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.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{750 - 580}{120}[/tex]
[tex]Z = 1.42[/tex]
[tex]Z = 1.42[/tex] has a pvalue of 0.9222
1 - 0.9222 = 0.0778
0.0778 = 7.78% of the population are considered to be potential leaders
