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 77.

(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1000 and $1400.

(b) If 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?

___ farms out of 28

Explanation / Answer

Ans:

Empirical rule:

a)As the limits 1000 and 1400 are one standard deviation away from the mean of 1200.

So,there are 68% of the farms ,whose land and building values per acre are between $1000 and $1400.

0.68*77=52.36

Hence, there are approximately 53 farms whose land and building values per acre are between $1000 and $1400.

b)0.68*25=17

Hence, there are approximately 17 farms out of 25 whose land and building values per acre are between $1000 and $1400.

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