the mean value of land and buildings per acre from a sample of farms is $1300, w

Question

the mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $200. The data set has a bell=shaped distibution. Assume the number of farms in the sample is 72.

use the emipirical rule to estimate the number of farms whose land and bulding valurs per acre are between $900 and $1700

___farms

If 22 additional farms were sampled, about how mane of these additional farms would you expect to have land and bulding values per acre are between %900 and $1700

___farms out of 22

Explanation / Answer

Given that the mean (u) of a normal probability distribution is 1300 and the
standard deviation (sd) is 200                  
About 68% of the area under the normal curve is within one standard deviation of the mean. i.e. (u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= [1300 ± 200]
= [ 1300 - 200 , 1300 + 200]
= [ 1100 , 1500 ]                  
About 95% of the area under the normal curve is within two standard deviation of the mean. i.e. (u ± 2s.d)
So to the given normal distribution about 95% of the observations lie in between
= [1300 ± 2 * 200]
= [ 1300 - 2 * 200 , 1300 + 2* 200]
= [ 900 , 1700 ]                  
About 99.7% of the area under the normal curve is within two standard deviation of the mean. i.e. (u ± 3s.d)
So to the given normal distribution about 95% of the observations lie in between
= [1300 ± 3 * 200]
= [ 1300 - 3 * 200 , 1300 + 3* 200]
= [ 700 , 1900 ]                  

a.
About 95% of the area under the normal curve is within two standard deviation of the mean [ 900 , 1700 ]

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