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