The mean value of land and buildings per acre from a sample of farms is $ 1600 ,

Question

The mean value of land and buildings per acre from a sample of farms is $ 1600 , with a standard deviation of $ 100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 78. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $ 1400 and $1800.

(b) If 25 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1400 per acre and $1800 per acre?

Explanation / Answer

a) for 1400 and 1800 are 2 std deviation away from mean ; therefore from empirical rule 95% of  of farms will lie between whose land and building values per acre are between $ 1400 and $1800.

therefore estimated number of farms =78*0.95=74.1

b) number of additional farms expected to have land and building values between $1400 per acre and $1800 per acre =0.95*25=23.75

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