Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher’s hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a normal model with μ = 91.75 mph and σ = 2.64 mph. Approximately what proportion of these four-seam fastballs would you expect to have speeds between 88 mph and 92.2 mph? (Express your answer as a decimal and round to 4 decimal places.) Approximately what proportion of these four-seam fastballs would you expect to have speeds above 92.2 mph? (Express your answer as a decimal and round to 4 decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 11% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 11%? (Round your answer to the nearest 0.1 mph.)
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.
Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher’s hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a normal model with μ = 91.75 mph and σ = 2.64 mph.
Approximately what proportion of these four-seam fastballs would you expect to have speeds between 88 mph and 92.2 mph? (Express your answer as a decimal and round to 4 decimal places.)
Approximately what proportion of these four-seam fastballs would you expect to have speeds above 92.2 mph? (Express your answer as a decimal and round to 4 decimal places.)
A baseball fan wishes to identify the four-seam fastballs among the fastest 11% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 11%? (Round your answer to the nearest 0.1 mph.)
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
