The mean value of land and buildings per acre from a sample of farms is $1200, w

Question

The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 79 (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1000 and $1400 farms (Round to the nearest whole number as needed ) (b #28 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1000 per acre and $1400 per acre? tarms out of 28 (Round to the nearest whole number as needed

Explanation / Answer

Mean = 1200

Sd = 200

Z = (X - mean) /sd

Z for 1000 = (1000-1200)/200 = - 1

Z for 1400 = (1400 - 1200)/200 = 1

According to empirical rule, mean + 1*sd covers 68% of area

So, P(1000 < X < 1400) = P(-1 < Z < 1) = 0.68

A) n = 79

Estimated number of farms = 79 * 0.68 = 53.72 = 54

B) n = 28

Estimated number of farms = 28 * 0.68 = 19.04 = 19

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