Question

If the probability of winning a slot machine is 5% and you are going to play 500 pulls. Using a normal approximation. What’s the probability that you win less than 40? What’s the probability that you win 30?

 

Answer 1

P = 0.05

1 - P = 0.95

n = 500

Here, BIN ( n , P ) that is , BIN (500 , 0.05)

According to normal approximation binomial,

X Normal

Mean = = n*P = 25

Standard deviation = =n*p*(1-p) = 23.75

We using continuity correction factor

The probability that you win less than 40

P(X < a ) = P(X < a - 0.5)

P(x < 39.5) = P((x - ) / < (39.5 - 25) / 23.75)

= P(z < 2.94)

Probability = 0.9984

The probability that you win 30

P(X = a) = P( a - 0.5 < X < a + 0.5)

P(29.5 < x < 30.5) = P((29.5 - 25)/ 23.75) < (x - ) /  < (30.5 - 25) / 23.75) )

= P(0.92 < z < 1.13)

= P(z < 1.13) - P(z < 0.92)

= 0.8708 - 0.8212

Probability = 0.0496