On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - NO 106 18 می می Hint b. Find the probability that a randomly selected person's IQ is over 114. 0.3284 answer to 4 decimal places. Exactly! Round your c. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest x Round your answer to 2 IQ score a child can have and still receive special services? 72.14 decimal places. Hmm?! Something isn't quite right. For this you are really looking at the 3 th percentile. d. Find the 25th and 75th percentiles (a.k.a Q1 and Q3) Round your answers to 2 decimal places. Q1: Q3: C
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - NO 106 18 می می Hint b. Find the probability that a randomly selected person's IQ is over 114. 0.3284 answer to 4 decimal places. Exactly! Round your c. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest x Round your answer to 2 IQ score a child can have and still receive special services? 72.14 decimal places. Hmm?! Something isn't quite right. For this you are really looking at the 3 th percentile. d. Find the 25th and 75th percentiles (a.k.a Q1 and Q3) Round your answers to 2 decimal places. Q1: Q3: C
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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![### Understanding IQ Distribution on a Distant Planet
On a planet far away from Earth, the IQ of the ruling species follows a normal distribution with a mean (\(\mu\)) of 106 and a standard deviation (\(\sigma\)) of 18. Suppose one individual is randomly chosen, and let \(X\) represent the IQ of an individual.
#### Problem Breakdown
**a. Distribution of \(X\):**
The IQ of individuals is normally distributed:
\[ X \sim N(106, 18) \]
**b. Probability of an IQ Over 114:**
To find the probability that a randomly selected person's IQ is over 114, calculate:
\[ P(X > 114) = 0.3284 \]
(Rounded to four decimal places)
**c. Determining Special Services Eligibility:**
A school offers special services for all children in the bottom 3% for IQ scores. Find the highest IQ score a child can have to still receive special services. This corresponds to the 3rd percentile.
The value provided (72.14) needs adjustment, as it was flagged as incorrect.
**d. Calculating Percentiles:**
To find the 25th percentile (Q1) and the 75th percentile (Q3), use statistical tables or software to round your answers to two decimal places.
These exercises help in understanding the application of normal distribution to real-world scenarios and decision-making processes based on statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b0cf1b8-84c6-4b32-890e-0885b2d3c430%2F8e549698-856d-4404-b642-bd736f0802bc%2Fo1ab69_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding IQ Distribution on a Distant Planet
On a planet far away from Earth, the IQ of the ruling species follows a normal distribution with a mean (\(\mu\)) of 106 and a standard deviation (\(\sigma\)) of 18. Suppose one individual is randomly chosen, and let \(X\) represent the IQ of an individual.
#### Problem Breakdown
**a. Distribution of \(X\):**
The IQ of individuals is normally distributed:
\[ X \sim N(106, 18) \]
**b. Probability of an IQ Over 114:**
To find the probability that a randomly selected person's IQ is over 114, calculate:
\[ P(X > 114) = 0.3284 \]
(Rounded to four decimal places)
**c. Determining Special Services Eligibility:**
A school offers special services for all children in the bottom 3% for IQ scores. Find the highest IQ score a child can have to still receive special services. This corresponds to the 3rd percentile.
The value provided (72.14) needs adjustment, as it was flagged as incorrect.
**d. Calculating Percentiles:**
To find the 25th percentile (Q1) and the 75th percentile (Q3), use statistical tables or software to round your answers to two decimal places.
These exercises help in understanding the application of normal distribution to real-world scenarios and decision-making processes based on statistical analysis.
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