### IQ Distribution and Statistics on a Distant Planet#### BackgroundOn a planet far away from Earth, the IQ of the ruling species is normally distributed with a mean of 103 and a standard deviation of 15. Suppose one individual is randomly chosen. Let \( X \) represent the IQ of an individual.#### Questions and Answers**a. What is the distribution of \( X \)?**The distribution of \( X \) is given by:\[ X \sim N(\text{mean}, \ \text{standard deviation}) \]Input the respective mean and standard deviation into this normal distribution formula.**b. Find the probability that a randomly selected person's IQ is over 92.**To find this probability, use the standard normal distribution. You can find the Z-score using the following formula: \[ Z = \frac{X - \mu}{\sigma} \]where \( \mu \) is the mean (103) and \( \sigma \) is the standard deviation (15). After calculating the Z-score for 92, you can use a Z-table or statistical software to determine the probability. Round your answer to 4 decimal places.**c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services?**To find this IQ score, you will need to determine the Z-score corresponding to the bottom 7% of the normal distribution. Use the inverse of the normal distribution (i.e., the Z-table) to find this value, then convert it back to the original IQ scale:\[ X = \mu + Z \sigma \]Round your answer to 2 decimal places.**d. Find the Inter Quartile Range (IQR) for IQ scores.**The IQR represents the range between the 25th percentile (Q1) and the 75th percentile (Q3). You can find Q1 and Q3 by looking up the Z-scores for 0.25 and 0.75, respectively, and converting these back to the original IQ scale.Calculate using the formulas:\[ Q1 = \mu + Z_{0.25} \sigma \]\[ Q3 = \mu + Z_{0.75} \sigma \]\[ \text{IQR} = Q3 - Q1 \]Round your answers to 2 decimal places.This section

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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 103 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person's IQ is over 92. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 103 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person's IQ is over 92. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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