00:01
For this problem to begin in part a we're asked for the expected value of r now if r is the number of winners in this situation we can see that based on the description for each individual they either win the grand prize or they don't and there's a limited number of people who? spin the wheel and each spin is independent.
00:24
So that means that we can model r as a binomial random variable with n equals equals 180, because there are 180 students spinning the wheel, and probability of success of 0 .04.
00:39
For any binomial random variable, the expected value is just n times p.
00:44
So in this case, it's going to be 4 % of 180.
00:49
Plugging in our values and calculating, 4 % of 180, 0 .04 times 180, is 7 .2.
00:58
For part , we're asked to find the standard deviation of r.
01:03
For a binomial random variable, the standard deviation is n times p times 1 minus p.
01:11
Plugging in our values and calculating that out, that's the square root of 180 times 0 .04 times 0 .96, for a result of 2 .629.
01:25
And for part c, we're asked to use the normal approximation to find the probability that more than 15 students win the grand prize.
01:32
So, probability of x greater than 15...