Question

On a planet far far away from earth l, IQ of the ruling species is normally distributed with a mean of 103 and a standard deviation of 16. Suppose one individual is randomly chosen. Let X=IQ of an individual

Find the Inter Quartile Range (IQR) for IQ scores.

Q1 ____

Q2___

Q3____

IQR___

Step 1

**The normal distribution:**

A continuous random variable *X* is said to follow normal distribution with mean µ and standard deviation σ if the probability density function of *X* is,

Step 2

**Find the distribution of X:**

Consider the variable IQ score of ruling species be denoted by *X.* It is given that the IQ score of ruling species is normally distributed.

The mean and standard deviation of IQ score of ruling species is *X-*bar = 103 and *s*(*X*) *= *16, respectively.

Here, the distribution of *X *is normal with mean 103 and standard deviation 16.

The probability density function of *X *is given below:

Step 3

**Quartiles of the normal distribution:**

*Three quartiles:*

- The first quartile separates the lowest 25% of the observations from the highest 75% of the observations. The first quartile is denoted by
*Q*1. - The second quartile separates the lower 50% of the observations from the highest 50% of the observations. The second ...

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