The mean value of land and buildings per acre from a sample of farms is $1700
with a standard deviation of $300
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
$1400 and $2000.
b)If 29 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1400 per acre and $2000 per acre?
Solution :
Given that,
mean = = $ 1700
standard deviation = = $ 300
n = 72
Using Empirical rule,
a) P( - < x < + ) = 68%
= P( 1700 - 300 < x < 1700 + 300 ) = 68%
= P( $1400 < x < $ 2000 ) =68%
= 72 * 0.68 = 48.96
= 49 farms
b) n = 29
= 29 * 0.68 = 19.72
= 20 farms
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