Question

The mean value of land and buildings per acre from a sample of farms is ​$1700 with a standard deviation of ​$200 The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 76 ​(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between ​$1300 and ​$2100 _____ farms ​(Round to the nearest whole number as​ needed.) ​(b) If 22 additional farms were​ sampled, about how many of these additional farms would you expect to have land and building values between ​$1300 per acre and ​$2100 ____ farms out of 22 ​(Round to the nearest whole number as​ needed.)

Answer 1

Let X denote the value of land and buildings per acre. Then

a)

Using the empirical rule, we know that 95% observations lie between and .

So, number of farms whose land and building values per acre are between ​$1300 and ​$2100 would be 0.95(76) = 72.2~72

b)

Similarly,

Number of additional farms whose land and building values per acre are between ​$1300 and ​$2100 would be 0.95(22) = 20.9~21