Question

The mean value of land and buildings per acre from a sample of farms is ​$1400​, 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 ​$1800. ​(Round to the nearest whole number as​ needed.) ​(b) If 27 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 ​$1800 per​ acre? ​(Round to the nearest whole number as​ needed.)

Answer 1

a)

The empirical rule says that approximately,

68% of data values lie within one standard of the population mean

95% of data values lie within two standards of the population mean

99.7% of data values lie within three standards of the population mean

Given:

Sample mean = 1400

Sample Standard deviation = 200

Hence approximately 95% of data values will lie within 1000 and 1800.

b)