Respuesta :
The percent of the population has an IQ over 115 is 15.87%.
What is z-score?
The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.
Using z tables, you may calculate the proportion of the population that is either below or above the score.
Now, according to the question;
IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.
A z score is determined as follows:
z = (x - μ)/σ
μ = mean of the distribution
σ = standard distribution of the sampling.
Calculation for the z score for x = 115
z = (115 - 100)/15
= 15/15
z = 1.0
Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,
P (x > 115) = 1 - P(x < 115)
= 1 - P(z < 1.0)
= 1 - 0.8413
P (x > 115) = 0.1587
Therefore, the percent of the population has an iq over 115 is 15.87%.
To know more about the z score, here
https://brainly.com/question/25638875
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