SOLUTION: 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 20% or mor

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Question 896380: 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 20% or more orange candies. Using a normal approximation, what is the probability that at least 20% of 300 randomly sampled candies will be orange?
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
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 20% or more orange candies. Using a normal approximation, what is the probability that at least 20% of 300 randomly sampled candies will be orange?
A:
Let X = number of candies that are orange in a sample of 300 candies.
The mean of X is 0.17(300) = 51
The variance of X is 0.17(1-0.17)(300) = 42.33
using normal distribution and applying the correction for continuity, the approximate probability is
P(X ≥ 59.5) = P(Z ≥ %2859.5+-+51%29%2Fsqrt%2842.33%29)
= P(Z ≥ 1.3065)
= highlight%280.0957%29