Question

The mean value of land and buildings per acre from a sample of farms is $1800 with a standard deviation of $200. The data set has a bell shaped distribution. Assume the number of farms in the sample is 79.   a.) Use the emprirical rule to etimate the number of farms whose landand buiding values per acre are between $ 1400 and $2200. ____farms ( round to nearest whole number) B.) If 20 additional farms were sampled about how many of these additional farms would you expect to have land and building values between $1400 and $2200 per acre. ____farms out of 20. (round to the nearest whole number)

Answer 1

Given,

= 1800 , = 200

According to emperical (68 - 95 - 99.7) rule,

Approximately 68% data falls in 1 standard deviation of the mean.

Approximately 95% data falls in 2 standard deviation of the mean.

Approximately 99.7% data falls in 3 standard deviation of the mean.

We have to calculate P( 1400 < X < 2200) = ?

Write 1400 in terms of and .

1400 = 1800 - 400

1400 = 1800 - 2 * 200

1400 = - 2 .

Similarly,

2200 = 1800 + 400

2200 = 1800 + 2 * 200

2200 =   + 2 .

2200 is 2 standard deviation above the mean.

That is 1400 and 2200 are 2 standard deviation of the mean.

farmAccording to emperical rule,

P(1400 < X < 2200) = 95%

a)

Of the 79 farm samples, number of farm are between $1400 and $2200

= 79 * 0.95

= 75.05

= 75

b)

Of the 20 additional farm, number of additional farm are between $1400 and $2200

= 20 * 0.95

= 19