4. The scatter plot shows the number of hits and home runs for 20 baseball players who had at least 10 hits last season. The table below shows the values for 15 of those players. The model, represented by y = 0.15x – 1.5, is graphed with a scatter plot. 40 30 10 100 150 200 hits Use the graph and the table to answer the questions. a. Player A had 154 hits in 2015. How many home runs did he have? How many was he predicted to have? b. Player B was the player who most outperformed the prediction. How many hits did Player B have last season? c. What would you expect to see in the graph for a player who hit many fewer home runs than the model predicted? hits home runs predicted home runs 12 2 0.3 22 1 154 26 145 11 1.8 21.6 20.3 110 16 15 57 3 7.1 149 17 20.9 29 2 2.9 13 0.5 18 1 1.2 86 15 11.4 163 31 23 115 13 15.8 57 16 7.1 96 10 12.9 home runs
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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