Question

Use the normal approximation to the binomal to find the probability for n=50, p=0.9 and X< or equal to 40. Round z value calculations to 2 decimal places and final answer To 4 decimal places

Answer 1

`\mathbb P(X\le40)\approx\mathbb P(X<40.5)\approx\mathbb P(Y<40.5)`

where
`Y` follows a normal distribution with mean
`np=45` and standard deviation
`√(np(1-p))\approx2.12`.


`\mathbb P(Y<40.5)=\mathbb P\left((Y-45)/(2.12)<(40.5-45)/(2.12)\right)=\mathbb P(Z<-2.12)`

where
`Z` follows the standard normal distribution. This probability is roughly 0.017003.