IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. This means the probability that a person has an IQ between a and b would be b 1 e-(x-100)²/450 dx. This is not an integral we can find by hand, so use a 15√2π Simpson's rule with n = 6 to approximate the probability that a person has an IQ between 140 and 200. Write your answer in percent form.
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. This means the probability that a person has an IQ between a and b would be b 1 e-(x-100)²/450 dx. This is not an integral we can find by hand, so use a 15√2π Simpson's rule with n = 6 to approximate the probability that a person has an IQ between 140 and 200. Write your answer in percent form.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Understanding Normal Distribution of IQ Scores**
IQ scores are normally distributed with a mean (average) of 100 and a standard deviation of 15. This implies that the probability of a person having an IQ between any two values, a and b, is given by the integral:
\[ \int_{a}^{b} \frac{1}{15\sqrt{2\pi}} e^{-\frac{(x-100)^2}{450}} \, dx \]
However, evaluating this integral by hand is not feasible. Instead, we can use Simpson's rule to approximate the probability. For this exercise, we will use Simpson's rule with \( n = 6 \) to estimate the probability that a person has an IQ between 140 and 200.
Write your answer in percent form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff015db4-0da8-42fc-9d60-01a672218c35%2F81eed411-dcb3-4536-9906-f1f930a24dec%2Ft3dg3xi_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Normal Distribution of IQ Scores**
IQ scores are normally distributed with a mean (average) of 100 and a standard deviation of 15. This implies that the probability of a person having an IQ between any two values, a and b, is given by the integral:
\[ \int_{a}^{b} \frac{1}{15\sqrt{2\pi}} e^{-\frac{(x-100)^2}{450}} \, dx \]
However, evaluating this integral by hand is not feasible. Instead, we can use Simpson's rule to approximate the probability. For this exercise, we will use Simpson's rule with \( n = 6 \) to estimate the probability that a person has an IQ between 140 and 200.
Write your answer in percent form.
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