Question

On a planet far far away from earth I, 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__

Answer 1

The interquartile range (IQR) for IQ scores can be calculated using Q1 and Q3. For this problem, Q1 is 77, Q3 is 129, and the IQR is 52.

Step-by-step explanation:

The interquartile range (IQR) for IQ scores can be calculated using the first quartile (Q1) and the third quartile (Q3). Q1 is the 25th percentile, and Q3 is the 75th percentile. To find Q1 and Q3, we can use the formula:

Q1 = Mean - (1.5 * Standard Deviation)

Q3 = Mean + (1.5 * Standard Deviation)

Given that the mean IQ is 103 and the standard deviation is 16, we can substitute these values into the formula:

Q1 = 103 - (1.5 * 16)

Q3 = 103 + (1.5 * 16)

Calculating these equations, we find that Q1 is 77 and Q3 is 129. The interquartile range (IQR) is the difference between Q3 and Q1, which is 52.