Problema Solution
the mean value of land and buildings per acre from a sample of farms is $1200,with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 78.
use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1300.
if 28 additional farms were samples about how many of these additional farms would you expect to have land and building values between #1100 per acre and $13000 per acres.
Answer provided by our tutors
The Empirical Rule applies to a normal, bell-shaped curve and states that within one standard deviation of the mean (both left-side and right-side) there is about 68% of the data; within two standard deviations of the mean (both left-side and right-side) there is about 95% of the data; and within three standard deviations of the mean (both left-side and right-side) there is about 99.7% of the data.
In our case $1100 and $1300 are within one standard deviation thus 68% of the data is in that interval:
78*0.68 = 47.6 or rounded to 48 of the farms have land and building values per acre between $1100 and $1300.
For the additional 28 farms we would expect that: 0.68*28 = 19 of these farm have land and building values between $1100 per acre and $13000 per acres.