my friend recently asked me this question but I do not know how to answer him. Could you help me out with it?
Everyday, John buys a $1 falafel sandwish at the food cart with a probability of 50%. Let F be the amount he spends on falafel sandwiches over the next 180 days. 1)Find E[F] and Var[F] 2)Approximate the likelihood that F>210
I got E[F] to be $90 but i cannot get Var[F] and isn't the likelihood that F>210 equals zero?
The distribution that is appropriate here is the binomial distribution with $n= 180$ and $p=0.5$. For that distribution the mean is $np =90$ and the variance is $np(1-P)= 90\cdot 0.5 = 45 $
I agree that $F$ being greater than 210 is impossible as the maximum value is 180. Perhaps what they are after is the normal approximation to the binomial distribution which allows you to answer questions like probability that money spent is $>110$ (a more sensible question!). Check out the normal approximation to the binomial - it should give a worked example you can follow.