Answer to Question #160115 in Statistics and Probability for Amber Heard

Question

The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $300. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 78.

a) Estimate the number of farms whose land and building values per acre are between $1300 and $1900. 

 

 

b) What percent of the farms have a value below $1900?

 

Answer 1

a) $P(1300<X<1900)=P(\frac{1300-1600}{300}<Z<\frac{1900-600}{300})=$

$=P(-1<Z<1)=P(Z<1)-P(Z<-1)=0.6826.$

Number of farms: $N=78*0.6826\approx53.$

b) $P(X<1900)=P(Z<\frac{1900-1600}{300})=P(Z<1)=0.8413.$