## Math 146 A Particular Fruit’S Weights Are Normally Distributed

1. A particular fruit’s weights are normally distributed, with a mean of 501 grams and a standard deviation of 37 grams. The heaviest 5% of fruits weigh more than how many grams?(Give your answer to the nearest gram. )2. Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 562 and standard deviation 93. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 19 and standard deviation 2. 4. (a) What is Elanor’s standardized score (z-score)?Round to 3 decimal places. (b) What is Gerald’s standardized score?Round to 3 decimal places. (c) Assuming that both tests measure the same kind of ability, who has the higher score?A. Gerald. B. Elanor. C. They both did equally well. 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 mean ? = 92. 12 mph and a standard deviation of ? = 2. 43 mph. 1. Compute the z-score of pitch with speed 90. 9 mph. (Round your answer to 2 decimal places. ) 2. Approximately what fraction of these four-seam fastballs would you expect to have speeds between 88. 6 mph and 96. 8 mph? (Express your answer as a decimal, not a percent, and round to 4 decimal places. ) 3. Approximately what fraction of these four-seam fastballs would you expect to have speeds above 96. 8 mph? (Express your answer as a decimal, not a percent, and round to 4 decimal places. ) 4. A baseball fan wishes to identify the four-seam fastballs among the slowest 19% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 19%? (Round your answer to the nearest 0. 1 mph. )

## MATH 146 A particular fruit’s weights are normally distributed

Question

1.A particular fruit’s weights are normally distributed, with a mean of 501 grams and a standard deviation of 37 grams.

The heaviest 5% of fruits weigh more than how many grams?(Give your answer to the nearest gram.)

2.Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 562 and standard deviation 93.

Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 19 and standard deviation 2.4.

(a) What is Elanor’s standardized score (z-score)?Round to 3 decimal places.

(b) What is Gerald’s standardized score?Round to 3 decimal places.

(c) Assuming that both tests measure the same kind of ability, who has the higher score?

A.Gerald.

B.Elanor.

C.They both did equally well.

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 mean ? = 92.12 mph and a standard deviation of ? = 2.43 mph.

1.Compute the z-score of pitch with speed 90.9 mph. (Round your answer to 2 decimal places.)

2.Approximately what fraction of these four-seam fastballs would you expect to have speeds between 88.6 mph and 96.8 mph? (Express your answer as a decimal, not a percent, and round to 4 decimal places.)

3.Approximately what fraction of these four-seam fastballs would you expect to have speeds above 96.8 mph? (Express your answer as a decimal, not a percent, and round to 4 decimal places.)

4.A baseball fan wishes to identify the four-seam fastballs among the slowest 19% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 19%? (Round your answer to the nearest 0.1 mph.)

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