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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___

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___

 

check_circleAnswer
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,

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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:

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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 Q1.
  • The second quartile separates the lower 50% of the observations from the highest 50% of the observations. The second ...

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