Question

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. 72 farms (round to the nearest whole number as needed.) (b) if 24 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 $2200 per acre? farms out of 24 (round to the nearest whole number as needed.)

Explanation:

Step1: Recall the empirical rule for normal distribution

For a bell - shaped (normal) distribution, about 95% of the data lies within 2 standard deviations of the mean. The mean is $\mu = 1800$ and the standard deviation is $\sigma=200$. $\mu - 2\sigma=1800 - 2\times200 = 1400$ and $\mu + 2\sigma=1800+2\times200 = 2200$. So, 95% of the data lies between 1400 and 2200.

Step2: Calculate the expected number for the new sample

We know that 95% of the data lies between 1400 and 2200. If we have a new sample of $n = 24$ farms, we find 95% of 24.
The calculation is $0.95\times24$.
$0.95\times24=22.8\approx23$

Answer:

23