Question

The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 73. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500. If 23 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1100 per acre and $1500 per acre?

Answer #1

(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500.

z(1100) = (1100-1300)/(100) = -2

z(1500) = (1500-1300)/(100 )= +2

p(1100-1500) = p(-2< z < +2) = 0.9545

Ans:: 0.9545*73 = 69.68 = **70 when rounded up**

If 23 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1100 per acre and $1500 per acre?

=0.9545*23 = 21.95 = **22 when rounded up**

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