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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

1) Is correct.

2) Is right.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

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

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

10) Is a good rounding of the answer.

11) Is correct.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

Thanks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

7) Needs work.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

8, too.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

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 01:09:11)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

That is correct!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

And I am getting 0.0062 for 8 as well.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

12 and 13 are correct!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

8) Is correct now too.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

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...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

9) Is good!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Hm? There is only one onswer for 6.

Here lies the reader who will never open this book. He is forever dead.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

12) Looks to be a good rounding.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

Thank-you both very much.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

3 is correct.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Again, what was your answer for 6?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

The exact answer for 6 is 0.46935 .

Here lies the reader who will never open this book. He is forever dead.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

0.4695 as an average of 0.470 and 0.469

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

I am not getting that for 6?!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,537

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

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