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the mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of $100. the data set has a bell shaped distribution. assume the number of farms if the sample is 70. use the empirical rule to estimate the number of farms whose land and building values per acre are between $1400 and $1600



Answer :

The sample mean is X[bar]=$1500

The sample standard deviation is S=$100

The sample size is n=70

The data set has a bell shaped distribution

The empirical rule states that

The values $1400 and $1600 are within one standard deviation away from the mean:

X[bar]+S=$1500+$100=$1600

X[bar]-S=$1500-$100=$1400

Following the rule you can expect 68% of the sample to be between them.

Whats left to do is to calculate the 68% of the sample

[tex]70\cdot0.68=47.6[/tex]

Around 47.6 of the farms have values per acre are between $1400 and $1600

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