Question

Let X be a random variable that is normally distributed with a mean of 10 and a

standard deviation of 2. Assume that a sample of 25 observations are taken from

this distribution, What is the interquartile range of the distribution of the sample

means.

Answer 1

Q1= $\mu$ - (0.675)*$\frac{\sigma}{\sqrt{n}}$

Q3=$\mu$ + (0.675)*$\frac{\sigma}{\sqrt{n}}$

Given $\mu$ = 10, $\sigma$ =2 and n=25.

Then,

Q1=$10-(0.675)\frac{2}{\sqrt{25}}$ =9.73

Q3= $10+(0.675)\frac{2}{\sqrt{25}}$ =10.27

The interquartile range (IQR) = Q3-Q1.

=10.27 - 9.73

=0.54

Answer: 0.54