document.write( "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?
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Q:
\n" ); document.write( "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?
\n" ); document.write( "A:
\n" ); document.write( "Let X = number of candies that are orange in a sample of 300 candies.
\n" ); document.write( "The mean of X is 0.17(300) = 51
\n" ); document.write( "The variance of X is 0.17(1-0.17)(300) = 42.33
\n" ); document.write( "using normal distribution and applying the correction for continuity, the approximate probability is
\n" ); document.write( "P(X ≥ 59.5) = P(Z ≥ $\"%2859.5+-+51%29%2Fsqrt%2842.33%29\"$ )
\n" ); document.write( " = P(Z ≥ 1.3065)
\n" ); document.write( " = $\"highlight%280.0957%29\"$ \n" ); document.write( "

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