binomial distribution, using cumulative distribution tables

• Mar 21st 2010, 10:57 AM
Tweety
binomial distribution, using cumulative distribution tables
The random variable X~B( 50, 0.40). Find

a) the largest value of k, such that $P(X\leq k)< 0.05$
B)the smallest number r, such that P(X>r) <0.01

I have done part 'a', by simply looking at the tables, n=50, p=0.40 and looking for the value for X that gives a probability less than 0.05. Which is k=13.

But I am stuck on part 'b', because it asks for x>r, and the tables only give values for $P(X\leq x )$

Can someone show me how to work this out?

Thanks.
• Mar 21st 2010, 12:09 PM
awkward
Quote:

Originally Posted by Tweety
The random variable X~B( 50, 0.40). Find

a) the largest value of k, such that $P(X\leq k)< 0.05$
B)the smallest number r, such that P(X>r) <0.01

I have done part 'a', by simply looking at the tables, n=50, p=0.40 and looking for the value for X that gives a probability less than 0.05. Which is k=13.

But I am stuck on part 'b', because it asks for x>r, and the tables only give values for $P(X\leq x )$

Can someone show me how to work this out?

Thanks.

Note that $P(X > r) = 1 - P(X \leq r)$.
• Mar 21st 2010, 12:17 PM
Tweety
Quote:

Originally Posted by awkward
Note that $P(X > r) = 1 - P(X \leq r)$.

Thank you,

But wouldn't I have to work out the value of 'r' before I do this?
• Mar 21st 2010, 06:25 PM
awkward
Quote:

Originally Posted by Tweety
Thank you,

But wouldn't I have to work out the value of 'r' before I do this?

No.

$P(X < r) < 0.01$

if and only if

$1 - P(X \leq r) < 0.01$

if and only if

$0.99 < P(X \leq r)$