Question

The probability of winning on a lot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution.

SHOW CLEARLY ALL WORK IN AN EASY WAY TO UNDERSTAND THANKS!

Answer 1

P( Winning) = 0.05 = p

n= 500

Mean = np= 0.05*500 = 25

variance= np(1-p) = 500*0.05*(1-0.05) =23.75

Let X be the number of winning

X~ N( 25, 23.75) [ normal approximation)

P( X = 30 ) = P( X< 30.5) [ using continuity correction]

= P( < )

= P( Z < 1.13)

= 0.87076