Cherry Pies. At one time, a well-known restaurant chain sold cherry pies. Professor D. Lund of the University of Wisconsin - Eau Claire enlisted the help of one of his classes to gather data on the number of cherries per pie. The data obtained by the students are presented in the following table. 0 1 2 1 0 2 3 0 0 2 1 4 1 2 1 1 0 1 3 2 0 0 0 0 1 0 2 1 1 0 1 2 2 1 4 a. For the student data, find the mean number of cherries per pie.b. For the student data, construct a relative-frequency distribution for the number of cherries per pie.c. Assuming that, for cherry pies sold by the restaurant, the number of cherries per pie has a Poisson distribution with the mean from part (a), obtain the probability distribution of the number of cherries per pie.d. Compare the relative frequencies in part (b) to the probabilities in part (c). What conclusions can you draw?
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.
Cherry Pies. At one time, a well-known restaurant chain sold cherry pies. Professor D. Lund of the University of Wisconsin - Eau Claire enlisted the help of one of his classes to gather data on the number of cherries per pie. The data obtained by the students are presented in the following table.
| 0 | 1 | 2 | 1 | 0 | 2 | 3 |
| 0 | 0 | 2 | 1 | 4 | 1 | 2 |
| 1 | 1 | 0 | 1 | 3 | 2 | 0 |
| 0 | 0 | 0 | 1 | 0 | 2 | 1 |
| 1 | 0 | 1 | 2 | 2 | 1 | 4 |
a. For the student data, find the mean number of cherries per pie.
b. For the student data, construct a relative-frequency distribution for the number of cherries per pie.
c. Assuming that, for cherry pies sold by the restaurant, the number of cherries per pie has a Poisson distribution with the mean from part (a), obtain the probability distribution of the number of cherries per pie.
d. Compare the relative frequencies in part (b) to the probabilities in part (c). What conclusions can you draw?
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