Maths - Statistics, cumulative probabilities

7) The random variable X~B(50, 0.40). Find:
a) the largest value of k such that P(X≤ k) < 0.05
b) the smallest number r such that P(X>r) < 0.01.
I don't understand how you do these questions, what is the method?
Thank you.

(edited 3 months ago)

Reply 1

mqb2766

Original post by murrayma767

Assuming you know how to calculate the usual cumulative probability for a binomial so something like calculate the probability that X is less than or equal to 10
P(X<=10)
then the questions are about the inverse cumulative, so calcuate the (largest) value k such that the cumulative probability is < 0.05
P(X<=k) < 0.05
Both are usually done on your calculator, but sometimes its worth sketching a rough distribution approximation for a simple verification.

(edited 3 months ago)

Reply 2

murrayma767

Ok, Thank you so what would I start by doing?

Reply 3

mqb2766

Original post by murrayma767

Ok, Thank you so what would I start by doing?

Which calculator are you using?

For insight, can you sketch the distribution - so use the usual formula to get the mean and std dev and note that
cumulative < 0.05
occurs at approximately
mean - 1.6 * std dev

Edit - assuming its a 991, you can list the usual cumulative probabilities
https://www.youtube.com/watch?v=g6BJGeq8sVc&ab_channel=MathsHelpwithMrOrys
(from ~3min onwards) and pick the one which is just less than 0.05.