According to a candy company packages of a certain candy con

According to a candy company, packages of a certain candy contain 17% orange candies. Find the approximate probability that the random sample of 300 candies will contain 19% or more orange candies.

Using a normal approximation, what is the probability that at least 19% of 300 randomly sampled candies will be orange?

Round the three decimal places as needed.

Solution

Normal Distribution
Proportion ( P ) =0.17
Standard Deviation ( )= Sqrt (P*Q /n) = 0.17*0.83/300
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.19) = (0.19-0.17)/0.0217
= 0.02/0.0217= 0.9217
= P ( Z <0.9217) From Standard Normal Table
= 0.8216                  

P( X>=0.19) = 1 - P(X < 0.19) = 1 - 0.8216 = 0.178