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

75

​(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between

​$1600

and

​$2000

 

nothing

farms ​(Round to the nearest whole number as​ needed.)

Answer 1

Given,

= 1800, = 200

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

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

Approximately, 95% of the data falls between 2 standard deviation of the mean

Approximately, 99.7% of the data falls between 3 standard deviation of the mean

We have to calculate P(1600 < X < 2000) = ?

We write 1600 in terms of and as

1600 = 1800 - 200

1600 = - 1

That is 1600 is 1 standard deviation below the mean.

Similarly,

2000 = 1800 + 200

2000 = + 1

2000 is 1 standard deviation above the mean.

That is 1600 and 2000 are 1 standard deviation of the mean.

According to emperical rule,

P(1600 < X < 2000) = 68%