Question

# On a planet far far away from Earth, IQ of the ruling species is normally distributed...

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 110 and a standard deviation of 17. 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 119. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 2% 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. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.

(c) X = 75.11

(d) We know that,

IQR = Q3 - Q1

Here, Q3 =

Q3 = 110 + 0.675 * 17

Q3 = 122.475

And

Q1 =

Q1 = 110 - 0.675 * 17

Q1 = 98.525

Now,

IQR = Q3 - Q1

IQR = 122.475 - 98.525

IQR = 23.95

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