he 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 in the sample is 80 (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between \( \$ 1300 \) and \( \$ 1700 \). 76 farms (Round to the nearest whole number as needed.) (b) If 21 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between \( \$ 1300 \) per acre and \( \$ 1700 \) per acre? farms out of 21 (Round to the nearest whole number as needed.)

According to the empirical rule, also known as the 68-95-99.7 rule, in a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean. Here, the mean is \( \$ 1500 \) and the standard deviation is \( \$ 100 \). Therefore, the range from \( \$ 1300 \) to \( \$ 1700 \) is one standard deviation below and above the mean. Since there are 80 farms in the sample, \( 0.68 \times 80 = 54.4 \), which we round to 54 farms. So, approximately 54 farms have land and building values per acre between \( \$ 1300 \) and \( \$ 1700 \). Now, when sampling an additional 21 farms, we still apply the empirical rule. Since we expect the same percentage (68%) to fall within that range, we calculate \( 0.68 \times 21 \approx 14.28 \), rounding to 14. Thus, we would expect about 14 additional farms to have values between \( \$ 1300 \) and \( \$ 1700 \) per acre.