In 1940 the average size of a U.S. farm was 174 acres. Let's say that the standard deviation was 52 acres. Suppose we randomly survey 37 farmers from 1940. Part (a) In words, define the random variable X. the number of U.S. farms the number of square feet of a U.S. farm the number of animals on a U.S. farm the number of acres of a U.S. farm Correct! The random variable of interest is the size of a U.S. farm, in acres. Part (b) In words, define the random variable X. the average number of farms in each state in the United States the average number of animals on a U.S. farm the average number of acres of a farm in the sample of 37 farmers the average number of square feet of a farm in the sample of 37 farmers Correct! The random variable of interest is the size of a farm, in acres. E Part (c) Give the distribution of X. (Round your standard deviation to two decimal places.) 174 8.55 E Part (d) The middle 50% of the distribution for X, the bounds of which form the distance represented by the IQR, lies between what two values? (Round your answers to two decimal places.) 174.00 acres (smaller value) 186.00 acres (larger value)

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.