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#1 2013-06-05 22:45:32

ShivamS
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Stats and Prob

1   What is the probability that an outcome z is less than -0.5?

0.3085

2   What is the probability that an outcome z is between -1 and 1.5?

0.7745

3   What would be the 91th percentile (P91) for such a N(0,1) distribution?

1.34

4   For a certain population diastolic blood pressure has been evaluated to have a mean value
of 75, a 10th percentile (P10) of 55, an 80th percentile (P80) of 90, and a range of 60. What
can we say for sure about diastolic blood pressure in that population?

Third quartile can't be more than 90.

According to a recent article in the journal "Appetite," 70% of 2 to 5 year old children
living in the US suffer from food neophobia. We choose at random five 2 to 5 year old
children living in the US.

5   What is the probability that at least four of the chosen children suffer from food
neophobia?

0.528

6   What is the probability that the number of children suffering from food neophobia
among the five chosen is between one and three, both inclusive?

0.6

According to a recent article in the journal "Environmental Health Perspectives," the
amount of soil ingested in one day by infants living in a particular town is a random
variable with a normal distribution with mean 20 g and variance 4. Assume that is
really the case.

7   What is the probability that an infant chosen at random from that town will ingest
more than 25 grams of soil in one day?

0.8944

8   What is the probability that an infant chosen at random from that town will ingest
less than 15 grams of soil in one day?

0.9876

9   Now assume that we chose at random 4 infants from that town. What is the
probability that none of them will ingest more than 25 grams of soil in one day?

0.9754

10   Suppose we flip a fair coin 10 times. What is the probability that we will get heads
every single time? 0.001

11   Now suppose we flip a coin that has heads on both sides. What is now the
probability that we will get heads every single time?   1, obviously.

A clinic has four departments, headed by doctor A, doctor B, doctor C, and doctor D,
respectively. Dr. A's department is treating 10 patients at this time, Dr. B's department is
treating 2 patients, Dr. C's department is treating 5 patients, and Dr. D's department is
treating 4 patients.
A patient from the clinic is chosen to be entered in a new clinical trial after informed
consent. The procedure to choose such a patient is the following: first a department in
the clinic is chosen at random, and then a patient from the chosen department is chosen
also at random.

12   What is the probability that John R, a patient treated by Dr. C, will be chosen to
enter the clinical trial?  0.05

13   What is the probability that Mary H., a patient in Dr. A's department, will be
chosen to enter the clinical trial?

0.025

One or two might be wrong so I need someone to check them. Reviewing for the final exam (our prof. gave me many pages like this). Thank-you in advance.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#2 2013-06-05 22:54:08

bobbym
Administrator

Online

Re: Stats and Prob

Hi;

1) Is correct.

2) Is right.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-06-05 22:54:44

ShivamS
Super Member

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Re: Stats and Prob

Okay, thanks. I realize they are a lot though.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#4 2013-06-05 22:58:10

anonimnystefy
Real Member

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Re: Stats and Prob

5 is correct and 6 is incorrect. I will check the others.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-06-05 22:59:30

bobbym
Administrator

Online

Re: Stats and Prob

10) Is a good rounding of the answer.

11) Is correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2013-06-05 23:03:12

ShivamS
Super Member

Offline

Re: Stats and Prob

Thanks.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#7 2013-06-05 23:06:08

bobbym
Administrator

Online

Re: Stats and Prob

7) Needs work.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#8 2013-06-05 23:07:50

anonimnystefy
Real Member

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Re: Stats and Prob

8, too.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#9 2013-06-05 23:08:15

ShivamS
Super Member

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Re: Stats and Prob

I did it again and got 0.0062. 7 that is. Now I will do 8. Getting 0.0062 for 8 too!

Last edited by Shivamcoder3013 (2013-06-05 23:09:11)


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#10 2013-06-05 23:08:53

bobbym
Administrator

Online

Re: Stats and Prob

That is correct!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#11 2013-06-05 23:09:31

ShivamS
Super Member

Offline

Re: Stats and Prob

And I am getting 0.0062 for 8 as well.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#12 2013-06-05 23:10:43

anonimnystefy
Real Member

Offline

Re: Stats and Prob

12 and 13 are correct!


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#13 2013-06-05 23:13:12

bobbym
Administrator

Online

Re: Stats and Prob

8) Is correct now too.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#14 2013-06-05 23:13:56

ShivamS
Super Member

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Re: Stats and Prob

Thanks everyone, is 8 correct now? And just saw Stefy say that 6 is wrong. Now I am getting for it (as there are two answers and I took the average). So many mistakes due to carelessness...


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#15 2013-06-05 23:15:40

bobbym
Administrator

Online

Re: Stats and Prob

Hi;

9) Is good!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#16 2013-06-05 23:15:49

anonimnystefy
Real Member

Offline

Re: Stats and Prob

Hm? There is only one onswer for 6.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#17 2013-06-05 23:17:15

ShivamS
Super Member

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Re: Stats and Prob

0.028 + 0.132 + 0.309 = 0.469 and = 0.472 – 0.002 = 0.470


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#18 2013-06-05 23:21:57

bobbym
Administrator

Online

Re: Stats and Prob

12) Looks to be a good rounding.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#19 2013-06-05 23:22:50

ShivamS
Super Member

Offline

Re: Stats and Prob

Thank-you both very much.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#20 2013-06-05 23:23:06

anonimnystefy
Real Member

Offline

Re: Stats and Prob

3 is correct.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#21 2013-06-05 23:25:21

bobbym
Administrator

Online

Re: Stats and Prob

Again, what was your answer for 6?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#22 2013-06-05 23:28:24

anonimnystefy
Real Member

Offline

Re: Stats and Prob

The exact answer for 6 is 0.46935 .


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#23 2013-06-05 23:28:27

ShivamS
Super Member

Offline

Re: Stats and Prob

0.4695 as an average of 0.470 and 0.469


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#24 2013-06-05 23:29:56

bobbym
Administrator

Online

Re: Stats and Prob

I am not getting that for 6?!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#25 2013-06-05 23:31:58

ShivamS
Super Member

Offline

Re: Stats and Prob

P(1 ≤ X ≤ 3) = P(X=1) + P(X=2) + P(X=3) = 0.028 + 0.132 + 0.309 = 0.469
Similarly, P(1 ≤ X ≤ 3) = P(X ≤ 3) – P(X ≤ 0) = 0.472 – 0.002 = 0.470


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

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