Math help... Please help me check my answers

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The following statistics are collected from the 2004/2005 NBA regular season.
- There are 397 basketball players in total
- 27 players have an average of at least 20 points per game (PPG)
- 40 players earn at least 10 million dollars annually
- 14 Players have an average of at least 20 PPG and earn at least 10 million dollars annually
A potential NBA player is interested in finding the relationship between PPG and salaries.

1a) What is the probability that a NBA player earns at least 10 million dollars annually if it is known that he has an average of at least 20 PPG?

b) What is the probability that a NBA player who has an average of less than 20 PPG or earns less than 10 million dollars annually is selected?


2. Nathan, who has never heard of any NBA players, is asked to complete an online survey. He has to choose a NBA player that best matches the description in each question. The survey contains 5 questions with the names of all the players in the 2004/2005 NBA regular season (397 basketball players in total) as choices. The producer of the survey defines success as choosing a player with an average of at least 20 PPG and an annual salary of over 10 million dollars. What is the probability of Nathan selecting at least 2 of these players on the survey assuming he randomly chooses a player for each question?

3. A new contest is available to NBA players. However, in order to make the game more interesting for the fans, only NBA players with an average PPG within 1.5 standard deviations from the mean PPG are eligible to participate. In the 2004/2005 NBA regular season, 13% of the players have at least 16 PPG and 16% have less than 3 PPG. If the PPG of players are assumed to be normally distributed, what percentage of the NBA players are eligible to participate in this contest? What is the minimum number of PPG that a player must have in order to enter the contest?

4. In order to compensate NBA players for their efforts in the 2004/2005 NBA regular season, the owners have put together 100 prizes. Players are randomly selected using a computer program and each player may get more than 1 prize. What is the probability that more than 75 prizes will be distributed to players earning less than 5 million dollars annually?

Answers:
1a: 0.5185
1b: ----
2: 0.0116
3: 0.8664, 5.5
4: 0.2843
 
Hello, an_mui!


The following statistics are collected from the 2004/2005 NBA regular season.
- There are 397 basketball players in total
- 27 players have an average of at least 20 points per game (PPG)
- 40 players earn at least 10 million dollars annually
- 14 Players have an average of at least 20 PPG and earn at least 10 million dollars annually

A potential NBA player is interested in finding the relationship between PPG and salaries.

1a) What is the probability that a NBA player earns at least 10 million dollars annually
if it is known that he has an average of at least 20 PPG?
Since he has an average <u>></u> 20 PPG, he is one of 27 players.

Among these 27 players, 14 earn <u>></u> $10M.

Therefore, the probability is: . 14/27 .= . 0.5185

b) What is the probability that a NBA player who has an average of less than 20 PPG
<u>or</u> earns less than 10 million dollars annually is selected?
"Less than 20 PPG <u>or</u> less than $10M" is the opposite of "More than 20 PPG <u>and</u> more than $10M"

Therefore, the probability is: . 1 - 14/397 .= .383/397
 
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