Question

The mean value of land and buildings per acre from a sample of farms is ​$1300 ​, with a standard deviation of ​$200 . The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 72 . ​(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between ​$1100 and ​$1500 . 49 farms ​(Round to the nearest whole number as​ needed.) ​(b) If 24 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? nothing farms out of 24 ​(Round to the nearest whole number as​ needed.) Statistics

Answer 1

a)

µ =    1300          
σ =    200          
we need to calculate probability for ,              
P (   1100   < X <   1500   )
=P( (1100-1300)/200 < (X-µ)/σ < (1500-1300)/200 )              
              
P (    -1.000   < Z <    1.000   )
about 68% of observation of data lie within 1 std dev away from mean

the number of farms whose land and building values per acre are between ​$1100 and ​$1500 = 72*0.68 = 48.96 ≈49 farms

b)

farms out of 24 = 24*0.68 = 16.32 ≈17 farms

(please try 16 if above gets wrong)