Question

Elizabeth Educationer is another cousin of Edith and Ella, but she likes to do things bigger than the other two.  She decides that she is going to sample 1000 televisions show, but she is also just going to rate them as either good or bad, just like her cousin, Ella. 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

Elizabeth Educationer is another cousin of Edith and Ella, but she likes to do things bigger than the other two.  She decides that she is going to sample 1000 televisions show, but she is also just going to rate them as either good or bad, just like her cousin, Ella. 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.        

n=1000, p=0.35

Expectation = np = 350

Variance = np(1 - p) = 227.5

Standard deviation = 15.0831

We have to find P( x≥500)

Z value for 500 with continuity correction, z=(499.5-350)/15.0831 =9.91

P( x≥500) = P( z > 9.91)

=0.0000