The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 71. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1200 and $2000. _____ 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 $1200 per acre and $2000 per acre? ______ farms out of 21 (Round to the nearest whole number as needed.)
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.
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