Problem Number One:
Scenario:
Kobe and his long time girlfriend Vanessa are miles apart. Kobe is in New Jersey while the love of his life is in Los Angeles. The only way they keep themselves updated is long distance calls. Kobe wants to change that, he finds out that this isn't going to work any longer, so he is thinking of moving to Los Angeles, but he just isn't quite sure as he has to make bigger decisions ahead of him.
Question:
The probability that Kobe will move to Los Angeles is 3/9, and the probability that he will marry Vanessa if he moves to Los Angeles is 11/20. The probability that he will marry Vanessa if he does not move to Los Angeles is 1/20.
(A) What is the probability that Kobe will move to Los Angeles and marry Vanessa?
(B) What is the probability that Kobe will NOT move to Los Angeles and still marry Vanessa?
(C) What is the probability that Kobe will NOT move to Los Angeles and NOT marry Vanessa?
First of all I would make a diagram that best describes the question you just read so here is how my diagram would look like for this situation.
So after drawing this diagram which best describes what the question is asking, which also shows my understanding of the question itself. You can now go ahead and answer the following questions.(A) What is the probability that Kobe will move to Los Angeles and marry Vanessa?
The answer would be:
The probability of Kobe moving to L.A. is 3/9, and the probability that Kobe will marry Vanessa if he moves to L.A. is 11/20.
How did you get that answer?
Well it`s simple, since the question asked what is the probability that Kobe will move to L.A. and marry Vanessa, you just simply follow the diagram above. So you would follow the diagram like this.
This picture above shows the probability of Kobe moving to L.A. which is 3/9 and the probability of Kobe marrying Vanessa if he moves to L.A. which is 11/20.
Moving on...
(B) What is the probability that Kobe will NOT move to Los Angeles and still marry Vanessa?
The answer would be:
The probability that Kobe will NOT move to L.A. is 6/9, and the probability that he will still marry Vanessa even though he does not move to L.A. is 1/20.
How did you get that answer?
Now you would take the diagram once again and follow the ``S`` way, because the question is asking what the probability is if Kobe will NOT move, meaning he will stay in N.J. but it is also asking what is the probability that he will still marry Vanessa even if he does stay in N.J. So simply follow the diagram like this:
This picture above shows the probability of Kobe staying in N.J. and NOT moving to L.A. which is 6/9, and also the probability that Kobe will marry Vanessa even though he stays in N.J. which is 1/20.
Moving on...
So now the final question:
(C) What is the probability that Kobe will NOT move to Los Angeles and NOT marry Vanessa?
The answer would be:
The probability that Kobe will NOT move to L.A. is 6/9, and the probability that Kobe will NOT marry Vanessa is 19/20.
How did you get that answer?
Now this question is asking what is the probability that Kobe will NOT move and NOT marry Vanessa, so now simply follow the same way but now your looking at the ``N`` because Kobe will NOT marry Vanessa.
This picture above shows the probability of Kobe NOT moving to L.A. which is 6/9 and NOT marry Vanessa which is 19/20. Since the question asked for probability of Kobe staying in N.J. and NOT marry Vanessa, this is how you would follow the diagram.Problem One Solved..
Problem Number Two:
Scenario:
Kobe played amazing in the 2000-01 season, he is one of the best competitive players in sports history. Kobe is one of the greatest players to ever step on the court, besides Michael Jordan. Kobe scored 50+ points 25 times in the year 2000-01.
Question:
Here is a table of Kobe's 50+ points in 25 games.
(A) Calculate the mean points and standard deviation.
(B) Determine the # of points one standard deviation below and one standard deviation above the mean.
(C) How many points are within one standard deviation of the mean?
So first of all I would grab my graphing calculator and set up the numbers, graphing calculator makes this question much easier to solve. So here we go.
Step by step set up getting the Standard Deviation, Mean, Median, Max, Min, and Total Sum:
Go to your list menu by pressing STAT then EDIT. (Below is a picture that kind of looks like the calculator buttons.)
Once you've arrived at your list menu, you would want to enter the numbers above into list 1.
You then want to exit to the home screen, and to do that, you just simply press 2ND then MODE to quit and put yourself to the home screen. (Below is a picture that kind of looks like the calculator buttons.)
When your on the home screen you then want to go STAT then RIGHT ARROW then ENTER and "1-Var Stats" will show up on your home screen then press 2ND then 1 (for your List 1, the numbers you just entered will be calculated). (Below is a picture that kind of looks like the calculator buttons.)
So now that you have the information you need to solve this question, you can now proceed and solve the question.
(A) Calculate the mean points and standard deviation.
The answer would be:
Mean = 55.68
Standard Deviation = 6.65
How did you get that answer?
Simply by looking at the information given by the calculator. If you follow this chart below.
The picture below is what you should have displayed on your calculator. (I excluded the other things that we won't be using.)
Moving on...
(B) Determine the # of points one standard deviation below and one standard deviation above the mean.
The answer would be:
# of points one standard deviation BELOW:
55.68 (Mean) - 6.65 (Std. Dev.) = 49
#of points one standard deviation ABOVE:
55.68 (Mean) + 6.65 (Std. Dev.) = 62.33
How did you get that answer?
So in the question it asked us one Std. Dev. ABOVE and BELOW the MEAN.
So to get one Std. Dev. ABOVE the MEAN, you must ADD one Std. Dev. to the MEAN.
Ex. Mean + Std. Dev.
55.68 + 6.65 = 62.33
And to get one Std. Dev. BELOW the MEAN, you must SUBTRACT one Std. Dev. from the MEAN.
Ex. Mean - Std. Dev.
55.68 - 6.65 = 49
(Careful with the signs.)
Moving on...
(C) How many points are within one standard deviation of the mean?
The answer would be:
You would have to count how many points are within one Std. Dev. of the mean. Which in this case the answer would be 23.
How did you get that answer?
To get one Std. Dev. of the mean, you would have to take one Std. Dev. ABOVE and BELOW the MEAN. So your range would become from 49 - 62.33. Now with that being said, you now have to check the chart.
If you count all the ones that have been crossed out, you get 23. The reason those numbers are crossed out is because they are in the range of 49 - 62.33. And that's what the question is asking us.
Scenario:
Kobe played amazing in the 2000-01 season, he is one of the best competitive players in sports history. Kobe is one of the greatest players to ever step on the court, besides Michael Jordan. Kobe scored 50+ points 25 times in the year 2000-01.
Question:
Here is a table of Kobe's 50+ points in 25 games.
(A) Calculate the mean points and standard deviation.(B) Determine the # of points one standard deviation below and one standard deviation above the mean.
(C) How many points are within one standard deviation of the mean?
So first of all I would grab my graphing calculator and set up the numbers, graphing calculator makes this question much easier to solve. So here we go.
Step by step set up getting the Standard Deviation, Mean, Median, Max, Min, and Total Sum:
Go to your list menu by pressing STAT then EDIT. (Below is a picture that kind of looks like the calculator buttons.)
Once you've arrived at your list menu, you would want to enter the numbers above into list 1.You then want to exit to the home screen, and to do that, you just simply press 2ND then MODE to quit and put yourself to the home screen. (Below is a picture that kind of looks like the calculator buttons.)
When your on the home screen you then want to go STAT then RIGHT ARROW then ENTER and "1-Var Stats" will show up on your home screen then press 2ND then 1 (for your List 1, the numbers you just entered will be calculated). (Below is a picture that kind of looks like the calculator buttons.)
So now that you have the information you need to solve this question, you can now proceed and solve the question.(A) Calculate the mean points and standard deviation.
The answer would be:
Mean = 55.68
Standard Deviation = 6.65
How did you get that answer?
Simply by looking at the information given by the calculator. If you follow this chart below.
The picture below is what you should have displayed on your calculator. (I excluded the other things that we won't be using.)
Moving on...
(B) Determine the # of points one standard deviation below and one standard deviation above the mean.
The answer would be:
# of points one standard deviation BELOW:
55.68 (Mean) - 6.65 (Std. Dev.) = 49
#of points one standard deviation ABOVE:
55.68 (Mean) + 6.65 (Std. Dev.) = 62.33
How did you get that answer?
So in the question it asked us one Std. Dev. ABOVE and BELOW the MEAN.
So to get one Std. Dev. ABOVE the MEAN, you must ADD one Std. Dev. to the MEAN.
Ex. Mean + Std. Dev.
55.68 + 6.65 = 62.33
And to get one Std. Dev. BELOW the MEAN, you must SUBTRACT one Std. Dev. from the MEAN.
Ex. Mean - Std. Dev.
55.68 - 6.65 = 49
(Careful with the signs.)
Moving on...
(C) How many points are within one standard deviation of the mean?
The answer would be:
You would have to count how many points are within one Std. Dev. of the mean. Which in this case the answer would be 23.
How did you get that answer?
To get one Std. Dev. of the mean, you would have to take one Std. Dev. ABOVE and BELOW the MEAN. So your range would become from 49 - 62.33. Now with that being said, you now have to check the chart.
If you count all the ones that have been crossed out, you get 23. The reason those numbers are crossed out is because they are in the range of 49 - 62.33. And that's what the question is asking us.Problem Two Solved..
