the mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of…

the mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of $200. the data set has a bell - shaped distribution. assume the number of farms in the sample is 74. (a) use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1900. 70 farms (round to the nearest whole number as needed.) (b) if 28 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1100 per acre and $1900 per acre? farms out of 28 (round to the nearest whole number as needed.)

the mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of $200. the data set has a bell - shaped distribution. assume the number of farms in the sample is 74. (a) use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1900. 70 farms (round to the nearest whole number as needed.) (b) if 28 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1100 per acre and $1900 per acre? farms out of 28 (round to the nearest whole number as needed.)

Answer

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 $\mu = 1500$ and the standard deviation $\sigma=200$. Calculate the bounds: $\mu - 2\sigma=1500 - 2\times200 = 1100$ and $\mu + 2\sigma=1500+2\times200 = 1900$. So, 95% of the data lies between 1100 and 1900.

Step2: Calculate the expected number for the new sample

We know that 95% of the data lies between 1100 and 1900. If we have a new sample of $n = 28$ farms, we find the number of farms in this range by multiplying the proportion (0.95) by the sample size. Let $x$ be the number of farms. Then $x=0.95\times28$. $x = 0.95\times28=26.6\approx27$

Answer:

27 farms out of 28