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<u>Answer-</u>
<u>Solution-</u>
The given data as follows,
After converting all the percentages and fractions to decimal, we can compare them all.
For converting percentages to decimal to divide the number by 100, so
Then converting the fraction into decimal,
As, all the numbers are converted into decimal, now comparing all the numbers,
Using the normal distribution, it is found that 0.0329 = 3.29% of the population are considered to be potential leaders.
In a <em>normal distribution</em> with mean and standard deviation
, the z-score of a measure X is given by:
- 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
.
- The standard deviation is of 125, hence
.
The proportion of the population considered to be potential leaders is <u>1 subtracted by the p-value of Z when X = 780</u>, hence:
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 brainly.com/question/24663213