Question

According to a candy​ company, packages of a certain candy contain 21​% orange candies. Find the approximate probability that the random sample of 500 candies will contain 23​% or more orange candies.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.210
sample size       =n=	500
std error of proportion=σp=√(p*(1-p)/n)=	0.0182

probability that the random sample of 500 candies will contain 23​% or more orange candies :

probability =

P(X>0.23)

=

P(Z>1.1)=

1-P(Z<1.1)=

1-0.8643=

0.1357

(try 0.1361 if this comes wrong due to rounding error)