Average height of players on a school basketball team. What height do basketball players need?
The manual contains 50 variants of standard tests measuring materials Main state exam (GIA-9).
The purpose of the manual is to develop students’ practical skills in preparation for the exam in mathematics (in new form) in 9th grade.
The collection contains answers to all variant tasks.
The manual is addressed to teachers and methodologists who use standard test tasks to prepare students for the Basic state exam(GIA-9) 2015, it can also be used by students for self-preparation and self-control.
Examples of test tasks:
19. A stationery store sells 138 pens, of which 34 are red, 23 are green, 11 are purple, there are also blue and black, there are equal numbers of them. Find the probability that when random selection one pen will be selected red or black pen.
20. The distance s (in meters) to the location of a lightning strike can be approximately calculated using the formula s = 330t, where t is the number of seconds that passed between the lightning flash and the thunderclap. Determine how far the observer is from the location of the lightning strike if t = 17. Give your answer in kilometers, rounded to the nearest whole number.
Answer:______________________________________
18. The average height of basketball players in the school men's team is 175 cm. The height of Kirill from the team is 175 cm. Which of the following statements is true?
1) There will definitely be a player, besides Kirill, 175 cm tall.
2) There will definitely be a player less than 175 cm tall.
3) There will definitely be a player, besides Kirill, at least 175 cm tall.
4) Kirill is the shortest in the national basketball team.
19. At a geometry exam, a student gets one problem from the collection. The probability that this problem is on the topic "Circle" is 0.45. The probability that this will be a problem on the topic “Area” is 0.25. There are no problems in the collection that simultaneously relate to these two topics. Find the probability that a student will get a task on one of these two topics in the exam.
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OGE-2018. Task No. 9 Statistics. Probability. TRAINING TASKS
1. In the cash and clothing lottery, for 100,000 tickets, 1,250 clothing and 810 cash winnings are drawn. What is the probability of winning money?
2. A stationery store sells 200 pens, of which 31 are red, 25 green, 38 purple, there are also blue and black, there are equal numbers. Find the probability that if one pen is chosen at random, either a red or a black pen will be chosen.
3. The dice are thrown twice. Find the probability that a number greater than 3 is rolled at least once.
4. On the plate are pies that look identical: 4 with meat, 8 with cabbage and 3 with cherries. Petya chooses one pie at random. Find the probability that the pie will contain cherries.
5. The shooter shoots at targets 3 times. The probability of hitting the target with one shot is 0.8. Find the probability that the shooter hit the targets the first 2 times and missed the last time.
OGE-2018. Task No. 9 Statistics. Probability. TRAINING TASKS
1. In the cash and clothing lottery, for 100,000 tickets, 1,250 clothing and 810 cash winnings are drawn. What is the probability of winning money?
2. A stationery store sells 200 pens, of which 31 are red, 25 green, 38 purple, there are also blue and black, there are equal numbers. Find the probability that if one pen is chosen at random, either a red or a black pen will be chosen.
3. The dice are thrown twice. Find the probability that a number greater than 3 is rolled at least once.
4. On the plate are pies that look identical: 4 with meat, 8 with cabbage and 3 with cherries. Petya chooses one pie at random. Find the probability that the pie will contain cherries.
5. The shooter shoots at targets 3 times. The probability of hitting the target with one shot is 0.8. Find the probability that the shooter hit the targets the first 2 times and missed the last time.
OGE-2018. Task No. 9 Statistics. Probability. TRAINING TASKS
1. In the cash and clothing lottery, for 100,000 tickets, 1,250 clothing and 810 cash winnings are drawn. What is the probability of winning money?
2. A stationery store sells 200 pens, of which 31 are red, 25 green, 38 purple, there are also blue and black, there are equal numbers. Find the probability that if one pen is chosen at random, either a red or a black pen will be chosen.
3. The dice are thrown twice. Find the probability that a number greater than 3 is rolled at least once.
4. On the plate are pies that look identical: 4 with meat, 8 with cabbage and 3 with cherries. Petya chooses one pie at random. Find the probability that the pie will contain cherries.
5. The shooter shoots at targets 3 times. The probability of hitting the target with one shot is 0.8. Find the probability that the shooter hit the targets the first 2 times and missed the last time.
ANSWERS AND EXPLANATIONS.
OGE-2018. Task No. 9 Statistics. Probability. TRAINING TASKS
1. 1. In the cash and clothing lottery, for 100,000 tickets, 1,250 clothing and 810 cash winnings are drawn. What is the probability of winning money?
Solution.
What is the probability of winning money?
2. 2. A stationery store sells 200 pens, of which 31 are red, 25 green, 38 purple, there are also blue and black, there are equal numbers. Find the probability that if one pen is chosen at random, either a red or a black pen will be chosen.
Solution.
Let's find the number of black handles: 
The probability that a red or black pen will be drawn is 
Answer: 0.42.
3. 3. The dice are thrown twice. Find the probability that a number greater than 3 is rolled at least once.
Solution.
When throwing a die, six different outcomes are equally possible. The event “more than three points will be rolled out” is satisfied in three cases: when the die rolls 4, 5, or 6 points. Therefore, the probability that no more than three points will appear on the die is equal to 
Thus, with one throw of a die, either event A is realized with equal probability - a number greater than 3 is rolled out, or event B - a number not greater than 3 is rolled out. That is, four events are equally likely to occur: A-A, A-B, B-A, B-B. Therefore, the probability that a number greater than 3 is rolled at least once is 
Answer: 0.75.
4. 4. On the plate are pies that look identical: 4 with meat, 8 with cabbage and 3 with cherries. Petya chooses one pie at random. Find the probability that the pie will contain cherries.
Solution.
There are 4 + 8 + 3 = 15 pies in total. Therefore, the probability that the chosen pie will have a cherry is equal to 
5. 5. The shooter shoots at targets 3 times. The probability of hitting the target with one shot is 0.8. Find the probability that the shooter hit the targets the first 2 times and missed the last time.
Solution.
The probability that the shooter will miss is 1 − 0.8 = 0.2. The probability that the shooter hit the targets the first two times is 0.8 2 = 0.64. Hence, the probability of an event in which the shooter first hits the target twice, and misses the third time is 0.64 · 0.2 = 0.128.
Answer: 0.128.
INDEPENDENT WORK.OGE-2018. Task No. 9 Statistics. Probability. IN 1
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INDEPENDENT WORK.OGE-2018. Task No. 9 Statistics. Probability. AT 2
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INDEPENDENT WORK.OGE-2018. Task No. 9 Statistics. Probability. AT 3
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INDEPENDENT WORK.OGE-2018. Task No. 9 Statistics. Probability. AT 4
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3. Petya, Vika, Katya, Igor, Anton, Polina cast lots as to who should start the game. Find the probability that the boy will start the game.
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Option #1
1. 1. Determine the probability that when throwing a dice (a fair dice) you will get less than 4 points.
Solution.
When throwing a die, six different outcomes are equally possible. The event “rolling less than four points” is satisfied in three cases: when the die rolls 1, 2 or 3 points. Therefore, the probability that the die will roll less than 4 points is
Answer: 0.5.
2. 2. Out of 1,400 new memory cards, an average of 56 are defective. What is the probability that a randomly selected memory card is working?
Solution.
The probability that the selected card will be faulty is 
Therefore, the probability that a randomly selected memory card is working is 1 − 0.04 = 0.96.
3. 3. Petya, Vika, Katya, Igor, Anton, Polina cast lots as to who should start the game. Find the probability that the boy will start the game.
Solution.
Answer: 0.5.
4. 4. The average height of basketball players on the school men's team is 175 cm. Kirill from this team is 175 cm tall. Which of the following statements is true?
1) There will definitely be a player, besides Kirill, 175 cm tall.
2) Kirill is the shortest in the national basketball team.
3) There will definitely be a player less than 175 cm tall.
4) There will definitely be a player, besides Kirill, at least 175 cm tall.
In your answer, write down the number of the selected statement.
Solution.
The first statement is incorrect: for example, a team can have three players with heights of 175 cm, 176 cm and 174 cm.
The second statement is incorrect: example from point 1.
The third statement is incorrect: all players can be 175 cm tall.
The fourth statement is true: since if there is a player shorter than 175 cm, then in order to average height was 175 cm. We need a player taller than 175 cm.
5. 5. Ninth-graders Petya, Katya, Vanya, Dasha and Natasha cast lots for who should start the game. Find the probability that Katya does not get the lot to start the game.
Solution.
There are five children in total, so the probability that the lot to start the game falls not on Katya, but on someone else is equal to 
Answer: 0.8.
OGE-2018. Task No. 9 Statistics. Probability.ANSWERS AND EXPLANATIONS. INDEPENDENT WORK.Option No. 2
1. On average, out of 150 flashlights that go on sale, three are faulty. Find the probability that a flashlight chosen at random in a store will turn out to be working.
Solution.
It is clear that out of 150 flashlights, 150 − 3 = 147 are working. Therefore, the probability that a flashlight chosen at random in a store will turn out to be working is equal to 
Answer: 0.98.
2. Kolya chooses a two-digit number at random. Find the probability that it ends in 3.
Solution.
There are a total of 90 two-digit numbers (numbers from 10 to 99 inclusive). There are only 9 two-digit numbers ending in 3. The probability of randomly choosing a two-digit number ending in 3 is equal to the ratio of the number of such two-digit numbers to the total number of two-digit numbers, that is 
Answer: 0.1.
3. Grandma has 10 cups: 7 with red flowers, the rest with blue. Grandmother pours tea into a randomly selected cup. Find the probability that it will be a cup with blue flowers.
Solution.
The probability that tea will be poured into a cup with blue flowers is equal to the ratio of the number of cups with blue flowers to the total number of cups. Total cups with blue flowers: 
Therefore, the desired probability 
Answer: 0.3.
4. 13 athletes from Russia, 2 athletes from Norway and 5 athletes from Sweden are participating in cross-country skiing. The order in which the athletes start is determined by lot. Find the probability that a non-Russian athlete will start first.
Solution.
In total there are 13 + 2 + 5 = 20 athletes. Therefore, the probability that a non-Russian athlete will start first is equal to 
Answer: 0.35.
5. There are 12 pies on the plate: 5 with meat, 4 with cabbage and 3 with cherries. Natasha chooses one pie at random. Find the probability that he ends up with a cherry.
Solution.
OGE-2018. Task No. 9 Statistics. Probability.ANSWERS AND EXPLANATIONS. INDEPENDENT WORK.Option No. 3
1. There are 60 tickets for the exam, Oleg didn't learn 12 of them. Find the probability that he will come across the learned ticket.
Solution.
Oleg learned 60 − 12 = 48 tickets. Thus, the probability that he will come across a learned ticket is equal to 
Answer: 0.8.
2. For the exam, tickets with numbers from 1 to 25 were prepared. What is the probability that a ticket chosen at random by a student has a number that is a two-digit number?
Solution.
A total of 25 tickets were prepared. Among them, 16 are double-digit. Thus, the probability of taking a ticket with a two-digit number is 
3. Determine the probability that when throwing a dice (a fair dice) you will get more than 3 points.
Solution.
When throwing a die, six different outcomes are equally possible. The event “more than three points are rolled” is met in three cases: when the die rolls 4, 5 or 6 points. Therefore, the probability that more than 3 points will appear on the die is
Answer: 0.5.
4. In a biology exam, a student gets one randomly selected question from a list. The probability that this question is about Arthropods is 0.15. The probability that it will be a Botany question is 0.45. There are no questions on the list that cover both of these topics at the same time. Find the probability that a student will get a question on one of these two topics in the exam.
Solution.
The probability of the sum of two incompatible events is equal to the sum of the probabilities of these events: 0.15 + 0.45 = 0.6.
Answer: 0.6.
5. The taxi company currently has 20 cars available: 9 black, 4 yellow and 7 green. One of the cars, which happened to be closest to the customer, responded to the call. Find the probability that a yellow taxi will come to him.
Solution.
The probability that a yellow car will arrive is equal to the ratio of the number of yellow cars to the total number of cars: 
Answer: 0.2.
OGE-2018. Task No. 9 Statistics. Probability.ANSWERS AND EXPLANATIONS. INDEPENDENT WORK.Option No. 4
1. There are identical-looking pies on the plate: 3 with meat, 3 with cabbage and 4 with cherries. Sasha takes one pie at random. Find the probability that the pie will contain cherries.
Solution.
The probability that a cherry pie will be chosen is equal to the ratio of the number of cherry pies to the total number of pies: 
2. The dice are thrown twice. Find the probability that the sum of two numbers drawn is odd.
Solution.
When rolling a die twice, there are 6 · 6 = 36 different outcomes. The sum is odd, if the first die rolls an odd number and the second rolls an even number, this corresponds to 3 · 3 = 9 outcomes. Or, if, on the contrary, an even number appears on the first die, and an odd number appears on the second, this corresponds to 3 · 3 = 9 outcomes. Therefore, the probability that the sum of two numbers drawn is odd is 
Answer: 0.5.
3. Petya, Vika, Katya, Igor, Anton, Polina cast lots as to who should start the game. Find the probability that the boy will start the game.
Solution.
The probability of an event is equal to the ratio of the number of favorable cases to the number of all cases. Favorable cases are 3 cases when Petya, Igor or Anton starts the game, and the number of all cases is 6. Therefore, the required ratio is
Answer: 0.5.
4. Ninth-graders Petya, Katya, Vanya, Dasha and Natasha cast lots for who should start the game. Find the probability that the boy will start the game.
Solution.
Of the five children, two are boys. Therefore the probability is equal 
Answer: 0.4.
5. Masha's TV is broken and only shows one random channel. Masha turns on the TV. At this time, three out of twenty channels show comedy films. Find the probability that Masha will end up on a channel where comedy is not shown.
Solution.
Number of channels that do not broadcast comedies 
The probability that Masha will not get on a channel that broadcasts comedies is equal to the ratio of the number of channels that do not broadcast comedies to the total number of channels:
Answer: 0.85.
OGE-2018. Task No. 9 Statistics. Probability.ANSWERS. INDEPENDENT WORK.
Option #1
Option No. 2
4. 0,35.
Option No. 3
Option No. 4
The criterion for a successful basketball player is: height that gives an advantage over shorter team members.
Therefore, this sport is considered the prerogative of tall people. The height of many basketball athletes is close to two meters.
Basketball rules
Basketball is an easy game to understand. The goal is to score more points than the opposing team scores. Points are calculated according to the following rules:
- A free throw gives one point.
- Shot from outside the three-point line - 2 points.
- Shot from behind the three-point line - 3 points.
Rules of the game:
- Basketball player is denied the ball lead with a fist, with both hands at the same time, touch with a foot and kick it.
- Player dribbling the ball You can’t push, hit on the hands, or trip.
- When an athlete dribbles the ball, he should not take it in both hands. If the athlete does this, then he can either pass to a teammate or shoot into the basket. After finishing the dribble, it is only permissible to take two steps with the ball in your hands.
- If the team member in possession of the ball steps outside the basketball court or hits the floor outside the court, it is considered that the ball goes out of bounds.
Attention! Basketball player It is forbidden to jump with a ball in your hands. If the player holding the ball nevertheless jumped with it in his hands, then before landing it is important to pass the ball to another team member or throw it into the hoop.
- The game is played until the score is reached 11, 15 or 21 points or limited in time - there are two options: two periods of 10-15 minutes or four periods of 7-10 minutes.
Reasons Why All Basketball Players Are So Tall
Most professional basketball athletes people who are much taller than average. But not only giants take up this sport.
Photo 1. Throwing the ball into a basketball basket. Since it is located quite high, it is easier for tall athletes to get into it.
Training helps increase the athlete's height: dynamic stretching, ball throwing, frequent jumping relieves stress on the spine and allows the skeleton to grow faster and easier. Therefore, the reason for being tall is not only genetic predisposition, but also regular training.
What height do basketball players need?
During the early days of the National Basketball Association, the average height of a basketball player was 188 cm, by 1980 this figure has increased up to 198 cm.
Nowadays the average height of a basketball player fluctuates from 195 to 198 cm. If we consider the indicators relative to the positions of the players, the average height of the point guards is 188 cm, and center 211 cm.
Why is the average height of players in the school men's team 175 cm?
Player height in school basketball teams not too different from the height of my classmates who are not part of the team.
Teenage basketball players who are part of the national team 16-17 years old, this figure is 175-177 cm.
What data do you need to take into this sport?
- Dexterity- the main quality that gives an athlete a decisive advantage in competition. The more dexterity, the better.
- Force: modern basketball has become a muscle sport. And now most players are actively training, realizing that in every match they will have to meet an opponent who knows exactly about hard strength training.
- Flexibility- the main factor in determining the limits of body movement.
- Speed: In basketball there are no movements that need to be performed for speed, but such a factor as the player’s speed of movement is important. As well as quick resourcefulness and speed of solution. After all, often in the game there are only a few seconds to accept it.
- Endurance: an athlete who has this quality is able to remain effective throughout the match.
- Maneuverability: In basketball, you need to quickly change your body position or direction of movement, depending on the situation on the field.
Useful video
Watch a video that explains how important player height is in basketball.
