The mean value of land and buildings per acre from a sample of farms is \( \$ 1200 \), with a standard deviation of \( \$ 300 \). The data set has a bell-shaped distribution Assume the number of fams in the sample is 76 (a) Use the empincal rule to estimate the number of farms whose land and buiding values per acre are between \( \$ 900 \) and \( \$ 1500 \). farms (Round to the nearest whole number as needed.) (b) If 30 additional farms were sampled, about how many of these adtibonal fams wouid vou expect to have land and building values between \( \$ 900 \) per acre and \( \$ 1500 \) per acre? \( \square \) farms out of 30 (Round to the nearest whole number as neecied)

To estimate the number of farms whose values per acre fall between $900 and $1500, we can apply the empirical rule, which states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Here, the mean is $1200, with a standard deviation of $300. Thus, between $900 ($1200 - $300) and $1500 ($1200 + $300), we can expect roughly 68% of the sample. For the first part (a), we calculate: \[ 0.68 \times 76 \approx 51.68 \] Rounding this gives us **52 farms**. For the second part (b), since the same percentage applies, we can expect the additional 30 farms also to follow this trend. So, estimating 68% of 30 gives us: \[ 0.68 \times 30 \approx 20.4 \] Rounding this, we would expect about **20 farms** out of the 30.