Question

Suppose that you bet $5 on each of a sequence of 50 independent fair games. Use the central limit theorem to approximate the probability that you will lose more than $75.

Answer 1

chances chances of happening = 0.0119

Explanation:

given data

bet = $5

independent fair games = 50

solution

we will think game as the normal distribution

so here mean is will be

mean =
`(50)/(2)`

mean = 25

and standard deviation will be

standard deviation =
`√(50*0.5*0.5)`

standard deviation = 3.536

so

we have to lose 33 out of 50 time for lose more than $75

so as chance of doing things z score is

z score =
`(33-25)/(3.536)`

z score = 2.26

so from z table

chances chances of this happening = 0.0119