Math Practice Problems - Batting Averages

Batting Averages - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=0

Answer the following questions about batting averages.

1.	In 328 at bats, a baseball player has a batting average of 0.230. In the next game, he has 6 at bats. What is the most likely number of hits he will get? Suppose he hits 0 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
2.	In 622 at bats, a baseball player has a batting average of 0.395. In the next game, he has 2 at bats. What is the most likely number of hits he will get? Suppose he hits 1 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:

Complexity=1

Answer the following questions about batting averages.

1.	In 366 at bats, a baseball player has a batting average of 0.150. In the next game, he has 3 at bats. What is the most likely number of hits he will get? Suppose he hits 2 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
2.	In 578 at bats, a baseball player has a batting average of 0.422. In the next game, he has 6 at bats. What is the most likely number of hits he will get? Suppose he hits 5 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:

Complexity=2

Answer the following questions about batting averages.

1.	In 478 at bats, a baseball player has a batting average of 0.192. In the next game, he has 3 at bats. What is the most likely number of hits he will get? Suppose he hits 1 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
2.	In 176 at bats, a baseball player has a batting average of 0.443. In the next game, he has 4 at bats. What is the most likely number of hits he will get? Suppose he hits 2 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:

Answers

Complexity=0

Answer the following questions about batting averages.

#	Problem	Correct Answer	Your Answer
1	In 328 at bats, a baseball player has a batting average of 0.230. In the next game, he has 6 at bats. What is the most likely number of hits he will get? Suppose he hits 0 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
Solution The player's batting average is 0.230 and the number of swings is 6. 0.230 × 6 = 1.38 which rounds to 1. Original total number of hits = batting average * total swings = 0.230 × 328 = 75. New total number of hits = original number of hits + number of hits at next game = 75 + 0 = 75. New total number of swings = original number of swings + number of swings at next game = 328 + 6 = 334. New batting average = new total number of hits / new total number of swings = 75 / 334 = 0.225.

#	Problem	Correct Answer	Your Answer
2	In 622 at bats, a baseball player has a batting average of 0.395. In the next game, he has 2 at bats. What is the most likely number of hits he will get? Suppose he hits 1 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
Solution The player's batting average is 0.395 and the number of swings is 2. 0.395 × 2 = 0.79 which rounds to 1. Original total number of hits = batting average * total swings = 0.395 × 622 = 246. New total number of hits = original number of hits + number of hits at next game = 246 + 1 = 247. New total number of swings = original number of swings + number of swings at next game = 622 + 2 = 624. New batting average = new total number of hits / new total number of swings = 247 / 624 = 0.396.

Complexity=1

Answer the following questions about batting averages.

#	Problem	Correct Answer	Your Answer
1	In 366 at bats, a baseball player has a batting average of 0.150. In the next game, he has 3 at bats. What is the most likely number of hits he will get? Suppose he hits 2 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
Solution The player's batting average is 0.150 and the number of swings is 3. 0.150 × 3 = 0.45 which rounds to 0. Original total number of hits = batting average * total swings = 0.150 × 366 = 55. New total number of hits = original number of hits + number of hits at next game = 55 + 2 = 57. New total number of swings = original number of swings + number of swings at next game = 366 + 3 = 369. New batting average = new total number of hits / new total number of swings = 57 / 369 = 0.154.

#	Problem	Correct Answer	Your Answer
2	In 578 at bats, a baseball player has a batting average of 0.422. In the next game, he has 6 at bats. What is the most likely number of hits he will get? Suppose he hits 5 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
Solution The player's batting average is 0.422 and the number of swings is 6. 0.422 × 6 = 2.532 which rounds to 3. Original total number of hits = batting average * total swings = 0.422 × 578 = 244. New total number of hits = original number of hits + number of hits at next game = 244 + 5 = 249. New total number of swings = original number of swings + number of swings at next game = 578 + 6 = 584. New batting average = new total number of hits / new total number of swings = 249 / 584 = 0.426.

Complexity=2

Answer the following questions about batting averages.

#	Problem	Correct Answer	Your Answer
1	In 478 at bats, a baseball player has a batting average of 0.192. In the next game, he has 3 at bats. What is the most likely number of hits he will get? Suppose he hits 1 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
Solution The player's batting average is 0.192 and the number of swings is 3. 0.192 × 3 = 0.576 which rounds to 1. Original total number of hits = batting average * total swings = 0.192 × 478 = 92. New total number of hits = original number of hits + number of hits at next game = 92 + 1 = 93. New total number of swings = original number of swings + number of swings at next game = 478 + 3 = 481. New batting average = new total number of hits / new total number of swings = 93 / 481 = 0.193.

#	Problem	Correct Answer	Your Answer
2	In 176 at bats, a baseball player has a batting average of 0.443. In the next game, he has 4 at bats. What is the most likely number of hits he will get? Suppose he hits 2 of those swings. What is his new batting average to three places?	Most likely number of hits: New batting average:
Solution The player's batting average is 0.443 and the number of swings is 4. 0.443 × 4 = 1.772 which rounds to 2. Original total number of hits = batting average * total swings = 0.443 × 176 = 78. New total number of hits = original number of hits + number of hits at next game = 78 + 2 = 80. New total number of swings = original number of swings + number of swings at next game = 176 + 4 = 180. New batting average = new total number of hits / new total number of swings = 80 / 180 = 0.444.

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