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)

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