The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 76. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500.

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cassandratiggs cassandratiggs

07-01-2018
Mathematics

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The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 76. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500.

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obenam obenam · Answer 1 · 2018-01-11T10:40:35+01:00

So we are looking to compute the following formula:
[tex]P(1100\ \textless \ X\ \textless \ 1500)= P(\frac{1100-1300}{100}\ \textless \ N\ \textless \ \frac{1500-1300}{100})\\=P(-2\ \textless \ N\ \textless \ 2)\text{ (Wherein N is the normal law (0,1))}.\\=0.95[/tex]

Answer: The probability is 0.95.
Now, in order to get the number of farms, multiply the whole number by the probability like this: 0.95*76 = 72.
Answer: 72 farms