Question

The mean value of land and buldings per acre from a sample of farms is $1600, with a standard doviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 70. (a) Use the empirical rulo to estimate the number of farms whose land and bulding values per acre are botwoen $1400 and $1800 ...........terms (Round to the nearest whole number as needed.)

Answer 1

Using the empirical rule and the provided data on land and buildings values, we estimate that approximately 68% of the farms fall within one standard deviation from the mean, roughly 48 farms have values between $1400 and $1800.

Step-by-step explanation:

The empirical rule, often referred to as the 68-95-99.7 rule, is a statistical rule which states that for a normal, bell-shaped distribution:

• Approximately 68% of the data falls within one standard deviation of the mean.
• Approximately 95% falls within two standard deviations.
• Approximately 99.7% falls within three standard deviations.

In the given situation, where the mean value of land and buildings per acre from a sample of farms is $1600 and the standard deviation is $200, we want to find the number of farms whose land and building values are between $1400 and $1800. This range is one standard deviation below and above the mean, so we can use the empirical rule to estimate that approximately 68% of the farms will fall within this range. Since there are 70 farms in the sample:

Number of farms = 0.68 × 70 = 47.6,

Rounded to the nearest whole number, we estimate that 48 farms have land and building values per acre between $1400 and $1800.