MHB How to Solve a Problem Using Binomial Distribution and Normal Table?

AI Thread Summary
To solve the problem using binomial distribution and normal approximation, the assignment requires calculating P(X<65) for X ~ B(100, 0.7). The mean and variance can be approximated as N(70, 21). The cumulative standard normal function, F, is then used to find P(X<65) by calculating F((65-70)/sqrt(21)), which yields approximately 0.1379 without continuity correction. However, applying a continuity correction gives a more accurate result of about 0.163. This approach effectively utilizes the normal distribution table for larger binomial problems.
isa2
Messages
2
Reaction score
0
I have an assignment
1z22b9f.png
which is a bit different,
I have to use Mathematics Handbook for Sience and Engineering to solve the problem,
I can look it up in tables. But the tables for binomial functions is only up to 20,
Normal Distribution to 3.4 and Poisson up to 24 in some cases.
So how do I do it? Approximation of some kind?
 
Last edited by a moderator:
Mathematics news on Phys.org
isa said:
I have an assignment image.png - Speedy Share - upload your files here which is a bit different,
I have to use Mathematics Handbook for Sience and Engineering to solve the problem,
I can look it up in tables. But the tables for binomial functions is only up to 20,
Normal Distribution to 3.4 and Poisson up to 24 in some cases.
So how do I do it? Approximation of some kind?

If you really want help try posting your question in a form that does not require helpers to jump through multiple hoops just to see it.

Your question is:

P(X<65) where X ~B(100,0.7)

CB
 
CaptainBlack said:
Your question is:

P(X<65) where X ~B(100,0.7)

CB

X is approximately ~N(70,21) (since the mean is Np and the variance is Np(1-p)), so P(X<65) ~= F((65-70)/sqrt(21)) where F denotes the cumulative standard normal, which is about 13.8%.

CB
 
CaptainBlack said:
X is approximately ~N(70,21) (since the mean is Np and the variance is Np(1-p)), so P(X<65) ~= F((65-70)/sqrt(21)) where F denotes the cumulative standard normal, which is about 13.8%.

CB

If I understan you corectly F((65-70)/sqrt(21)) = F(1.09108..)? And then look it up in the Normal table witch is 0.8621 or 0.8643 I'm not quite sure.
And then take 1-0.8621 and you get 0.1379?
Is that how you do it?

You do not have to include F((0-70)/sqrt(21)) ?
Since it is < 65? so like F((65-70)/sqrt(21)) -F((0-70)/sqrt(21))?
 
isa said:
If I understan you corectly F((65-70)/sqrt(21)) = F(1.09108..)? And then look it up in the Normal table witch is 0.8621 or 0.8643 I'm not quite sure.
And then take 1-0.8621 and you get 0.1379?
Is that how you do it?

You do not have to include F((0-70)/sqrt(21)) ?
Since it is < 65? so like F((65-70)/sqrt(21)) -F((0-70)/sqrt(21))?

More or less, but a continuity correction may be appropriate:

The continuity corrections would give F( (65.5-70)/sqrt(21) ) ~= 0.163

CB
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

Similar threads

Back
Top