Answer :
Approximately 13.59% of adults have an IQ score between 115 and 125. The closest answer choice is 13.5%.
To find the percentage of adults with an IQ score between 115 and 125, we can use the properties of the normal distribution and the empirical rule (68-95-99.7 rule).
The IQ score is normally distributed with a mean (μ) of 105 and a standard deviation (σ) of 10.
According to the empirical rule:
Approximately 68% of the data falls within one standard deviation (σ) from the mean (μ).
Approximately 95% of the data falls within two standard deviations (2σ) from the mean (μ).
Approximately 99.7% of the data falls within three standard deviations (3σ) from the mean (μ).
To find the percentage of adults with an IQ score between 115 and 125, we can use the cumulative probability function for the normal distribution:
P(115 ≤ X ≤ 125) = P(Z ≤ (125 - μ) / σ) - P(Z ≤ (115 - μ) / σ)
where Z is the standard normal random variable.
Calculations:
P(115 ≤ X ≤ 125) = P(Z ≤ (125 - 105) / 10) - P(Z ≤ (115 - 105) / 10)
P(115 ≤ X ≤ 125) = P(Z ≤ 2) - P(Z ≤ 1)
P(115 ≤ X ≤ 125) = 0.9772 - 0.8413
P(115 ≤ X ≤ 125) ≈ 0.1359
Therefore, approximately 13.59% of adults have an IQ score between 115 and 125. The closest answer choice is 13.5%.
To know more about standard deviation, visit:
https://brainly.com/question/13498201
#SPJ11
