Respuesta :
Using the normal distribution, it is found that 0.0329 = 3.29% of the population are considered to be potential leaders.
In a normal distribution 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]
- It 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, which is the percentile of X.
In this problem:
- The mean is of 550, hence [tex]\mu = 550[/tex].
- The standard deviation is of 125, hence [tex]\sigma = 125[/tex].
The proportion of the population considered to be potential leaders is 1 subtracted by the p-value of Z when X = 780, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{780 - 550}{125}[/tex]
[tex]Z = 1.84[/tex]
[tex]Z = 1.84[/tex] has a p-value of 0.9671.
1 - 0.9671 = 0.0329
0.0329 = 3.29% of the population are considered to be potential leaders.
To learn more about the normal distribution, you can take a look at https://brainly.com/question/24663213
