The mean value of land and buildings per acre from a sample of farms is $1200 ,

Question

The mean value of land and buildings per acre from a sample of farms is $1200 , with a standard deviation of $100 . The data set has a bell-shaped distribution. Assume the number of farms in the sample is 70 . (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1000 and $1400 . nothing farms (Round to the nearest whole number as needed.) (b) If 30 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 $1400 per acre? nothing farms out of 30 (Round to the nearest whole number as needed.)

Explanation / Answer

Note that the distribution need to be both bell-shaped and symmetrical before you can use the empirical rule.

(a)

mean = 1200
Std Dev = 100

Let X = value of lands and buildings of farm per acre
P(1000 < X < 1400)
= P(-2< Z < 2)

From the empirical rule, 95% of the farms have lands and buildings which are between $1000 and $1400 per acre.

(b)

Number of farms
= 95% x 30
= 0.95 x 30
= 28.5

=29 (rounded off to nearest whole number)

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