Question

Between may 3, 2009 and june 2, 2012, 56% of kickstarter pitches were unsuccessful. What is the probability that, in a random sample of 50 kickstarter projects that more than 50% would have been successful.

I need actaul steps to solve this to know where I get the numbers to understand the problem not an Exel program.

Answer 1

Probability that kickstarter pitches are unsuccessful = 0.56

Let this Probability be q.

So, Probability of a kickstarter pitcher being successfu = p = 1-q = 1-0.56 = 0.44

Let X be the number of kickstarter projects that is successful.

So, X follows a binomial distribution with parameters n and p.

Since we have two possible options (success (p) and failure (q))

Given, n = 50

So, X ~ Bin (n,p) or, X~Bin(50, 0.44)

Since we need the probability of 50% of the projects out of 50 samples to be successful.

We basically need the probability that more than 25/50 people are successful.

So, P(X>25)

Since n is large, let us do normal approximation -

X~N(np,npq) approximately

E(X) = = np = 50×0.44 = 22

V(X) = = npq = 50×0.44×0.56 = 12.32

So,

Where Z follows standard normal distribution I.E., X ~ N(0,1)

Thus, we need -

P(Z > 0.71225)

Using statistical tables we can see that P(Z<0.71225) is 0.762

So, P(Z>0.7125) = 1-0.762 = 0.238.