# Thread: [SOLVED] Statistics - Binomial Distribution

1. ## [SOLVED] Statistics - Binomial Distribution

Question:
Given that D~B(12,0.7), calculate the smallest value of d such that P(D>d)<0.90

n = 12, p = 0.7, q = 1 - 0.7 = 0.3, d=?

2. I may be guilty of promoting myself here....but it's not for profit so I think it's OK.

If you look in the MHF software forum you will find a little program I wrote. I think it would be useful to you.

You can get the answer to your problem using the program but that's not really the point.

If you play around with it a little you might understand the question better.

As for answering the question properly...

Do you know how to calculate P(D=0) or P(D=1) for example?

3. Yes, I know how to calculate P(D=0)
P(D=0) = 12C0 * 0.7^0 * 0.3^(12-0)
= 1 * 1 * 0.000000531
= 0.000000531
I don't know how to get the value of d!

4. Originally Posted by looi76
Question:
Given that D~B(12,0.7), calculate the smallest value of d such that P(D>d)<0.90

n = 12, p = 0.7, q = 1 - 0.7 = 0.3, d=?
It wants you to find the samllest $\displaystyle d$ such that:

$\displaystyle P(D>d)<0.90$

where:

$\displaystyle P(D>d)= \sum_{r=d+1}^{12} b(r;12,0.7) <0.9,\ d$ an integer $\displaystyle \le 12$

where $\displaystyle b(r;12,0.7)$ is the probability of exactly $\displaystyle r$ successes in $\displaystyle 12$ Bernoulli trials with a single trial probability of success of $\displaystyle 0.7$

Now work backwards from $\displaystyle 12$ adding probabilities untill the total is greater than $\displaystyle 0.9$, and that last term is your $\displaystyle d$

RonL