Question

In a certain county, the sizes of family farms approximately follow mound-shaped (normal) distribution with a mean of 472 acres and a standard deviation of 27 acres.

(a) According to the empirical rule, approximately __% of family farms have a size between 418 and 526 acres.

(b) According to the empirical rule, approximately __% of family farms have a size between 391 and 553 acres.

(c) According to the empirical rule, approximately __% of family farms have a size between 445 and 499 acres.

Answer 1

Given , sizes of family farms ( X ) approximately follow mound-shaped (normal) distribution with a mean = 472 acres and a standard deviation = 27 acres.

According to Empirical rule -

1 ) 68% of the data fall within one standard deviation.

In mathematical notation, this is represented as:

2) 95% fall within two standard deviations.

In mathematical notation, this is represented as:

3) 99.7% fall within three standard deviations

In mathematical notation, this is represented as:

Graphically explanation :

Here we are given , = 472 , = 27

Let's answer questions using above diagram

a ) According to the empirical rule, approximately 95 % of family farms have a size between 418 and 526 acres

b) According to the empirical rule, approximately 99.7% of family farms have a size between 391 and 553 acres.

c) According to the empirical rule, approximately 68% of family farms have a size between 445 and 499 acres.