Answer to Question #148736 in Statistics and Probability for Rebekah

Question

Assume the number of farms in the sample is 40. Estimate the number of farms whose land and building values per acre are between $1500 and $3300

Answer 1

 The mean value of land and buildings per acre from a sample of farms is $2400, with a standard deviation of $450. The data set has a bell shaped distribution. Assume the number of farms in the sample is 40.

Use the Emperical Rule to estimate the number of farms whose land and building values per acre are between $1500 and $3300.

Emperical Rule holds only for normal population: approximately $95.45\%$ population lies within 2 standard deviation

$$(\mu-2\sigma, \mu+2\sigma)=(2400-2(450), 2400+2(450))$$

$$=(1500, 3300)$$

$$40\cdot0.9545\approx38$$

$$P(1500<X<3300)$$

$$=P(\dfrac{1500-2400}{450}<Z<\dfrac{3300-2400}{450})$$

$$=P(-2<Z<2)\approx0.97725-0.02275$$

$$\approx 0.9545$$

38 farms.