Question
The mean value of land and buildings per acre from a sample of farms is $1500...
The mean value of land and buildings per acre from a sample of farms is $1500 , with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 71. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $1700
Homework Answers
Answer #1
Emperical Rule ( 68 - 95 - 99.7) states that,
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.
Given 
= 1500, 
=
100
We have to find P( 1300 < X < 1700) = ?
1300 = 1500 - 2 * 100
That is
1300 = - 2 *
That is 1300 is 2 standard deviation below the mean.
Similarly,
1700 = + 2 *
That is 1700 is 2 standard deviation above the mean.
So, 1300 and 1700 are 2 standard deviation below and above the mean, that is 2 standard deviation of the mean.
By emperical rule, approximately 95% of the data falls in the 2 standard deviation of the mean.
P( 1300 < X < 1700) = 0.95
So in 71 samples, number of farms falls between $1300 and $1700 is
0.95 * 71 = 0.6745
= 68 (Rounded to nearest integer)
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