Question

The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $300. 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 $1400 and S2000toms (Round to the newest whole number as needed)() 11 28 additional terms were sampled about how many of these additional farms would you expect to have land and building values between $1400 per acre and S2000 per acre?farms out of 28 (Round to the nearest whole number as needed)

Answer 1

Solution

For this case we know that:

$\mu=1700,\sigma=300$

Part a

We can find the deviations from the mean in the following way:

$\frac{1400-1700}{300}=-1,\frac{2000-1700}{300}=1$

We know that 1 deviation within the mean we have 68% of the values then the answer is:

71* 0.68= 48.28

Rounded would be 48

Part b

The new total of farms are: 28 + 71= 99

Then the new value is:

99 *0.68 = 67.32

Rounded would be 67