Question

29. The mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of $200. The data set has a bell-shaped distribution. Estimate the percent of farms whose land and building values per acre are between $1300 and $1700.

Answer 1

Answer: 68.27%

Step-by-step explanation:

Given : Mean value of land and buildings per acre from a sample of farms :

$\mu=\ 1500$

$\sigma= \ 200$

The data set has a bell-shaped distribution. i.e. it follows Normal distribution.

Using $z=\dfrac{x-\mu}{\sigma}$ , for x= 1300 , we have

$z=\dfrac{1300-1500}{200}=-1$

For x= 1700 , $z=\dfrac{1700-1500}{200}=1$

Using standard normal z-value table,

P-value = P(-1<z<1)=$1-2P(z>|1|)=1-2(0.1586553)=0.6826894\approx0.6827$  [Round to nearest 4 decimal places.]

i.e. The percent of farms whose land and building values per acre are between $1300 and $1700 = 68.27%