91Ó°ÊÓ

A random variable is a variable whose potential qualities are mathematical results of an irregular peculiarity. There are two kinds of irregular factors, discrete and nonstop.

a. The size of the US farms is defined as X

b. The average size of the US farm after surveying $38$farms

c. Given,

The standard deviation $\mathrm{σ}$=$55$

Sample size n = $38$

and Mean $\mathrm{μ}=174$

From the formula,

$$\begin{gathered} \stackrel{¯}{=X}~N\left({\mathrm{μ}}_x,\frac{{\mathrm{σ}}_x}{\sqrt{n}}\right) \\ =\stackrel{¯}{X}~N\left(174,\frac{55}{\sqrt{38}}\right) \\ =\stackrel{¯}{X}~N(174,8.922) \end{gathered}$$

d. Given,

The standard deviation $\mathrm{σ}=55$

Sample size n =$38$

and Mean = $\mathrm{μ}=174$

$\stackrel{¯}{X}~N(174,8.922)$

First quartile is$25th$percentile

Hence, $P(\stackrel{¯}{x}<k)=0.25$

The value of k using a calculator is,$168$acres

The third quartile is $75th$percentile

Hence, $P(\stackrel{¯}{x}<k)=0.75$

The value of k using a calculator is, $\text{invnorm}(0.75,174,8.922)=180$acres

Thus the IQR is from$168-180$acres