A sample of 20 students is asked if they prefer Coke or Pepsi.Suppose that in th

Question

A sample of 20 students is asked if they prefer Coke or Pepsi.Suppose that in the population, 80% prefer Coke. Find theprobability that more than 2/3 of students in the sample preferCoke.

a) Can we use the normal distribution to approximate probabilities?

b) What if we ask 200 students ?

Thanks so much for time and help !

Explanation / Answer

We generally follow the rule that we can use a normal approximationif np>10 and n(1-p)>10. In this case, np = 20(.8) = 16, and n(1-p) = 20(.2) =4, so sincethey're not both bigger than 10, we would NOT be able to use thenormal approximation. If n were switched to 200, we WOULD be able to use the normaldistribution. To calculate the probability that more than 2/3 of the 20 prefercoke, we would sum the binomial probabilities from 14-20 of thestudents prefering Coke binompdf(20,.8,14) + binompdf(20,.8,15) + ... + binompdf(20,.8,20)= .9133

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