the mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of…
the mean value of land and buildings per acre from a sample of farms is $1800, with a standard deviation of $200. 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 $1400 and $2200. farms (round to the nearest whole number as needed.)
Answer
Explanation:
Step1: Calculate number of standard - deviations
First, find how many standard - deviations $1400$ and $2200$ are from the mean. The mean $\mu = 1800$ and the standard deviation $\sigma=200$. For $x = 1400$, $z_1=\frac{1400 - 1800}{200}=\frac{- 400}{200}=-2$. For $x = 2200$, $z_2=\frac{2200 - 1800}{200}=\frac{400}{200}=2$.
Step2: Apply the empirical rule
The empirical rule for a normal (bell - shaped) distribution states that approximately $95%$ of the data lies within $z=-2$ and $z = 2$.
Step3: Calculate the number of farms
We have a sample of $n = 76$ farms. The number of farms within the range is $0.95\times n$. So, $0.95\times76=72.2$.
Answer:
72