Question

Elizabeth Educationer is interested in the quality of the children’s television programs. She decides that she is going to sample 1000 televisions show and she is going to rate them as either good or bad.  She agrees that the probability that a show will be rated as good is equal to p = .35. Find the probability that at least half of the shows will be rated as good.  This follows a binomial distribution, but because of the sample size, we will need to use the normal approximation to the binomial in order to answer this question.        

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Sample size, n = 1000

P(a show will be rated as good), p = 0.35

q = 1 - p = 0.65

Mean = np

= 1000 x 0.35

= 350

Standard deviation = Vmpq

= V1000 x 0.35 x 0.65

= 15.08

P(at least half of the shows will be rated as good) = P(X \small \geq 500)

= 1 - P(X < 499.5)

= 1 - P(Z < (499.5 - 350)/15.08)

= 1 - P(Z < 9.91)

= 1 - 1

= 0

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