MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer: 68.27%Step-by-step explanation:Given : Mean value of land and buildings per acre from a sample of farms :[tex]\mu=\$1500[/tex][tex]\sigma= \$200[/tex] The data set has a bell-shaped distribution. i.e. it follows Normal distribution.Using [tex]z=\dfrac{x-\mu}{\sigma}[/tex] , for x= 1300 , we have[tex]z=\dfrac{1300-1500}{200}=-1[/tex] For x= 1700 , [tex]z=\dfrac{1700-1500}{200}=1[/tex] Using standard normal z-value table,P-value = P(-1<z<1)=[tex]1-2P(z>|1|)=1-2(0.1586553)=0.6826894\approx0.6827[/tex] Β [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%