6.Suppose that 12% of children in a certain population have a serious food allergy. A simple random sample of 200 children are selected form this population.

a. Calculate the standard deviation of p^, the proportion of children with serious food allergies in the sample. And explain what the number means in the context of the problem. [3 marks]

b. Can we use the central limit theorem to say that the sample proportion, p^, has an approximately

Normal distribution? Justify your answer. [2 marks]

c.Calculate the probability of finding more than 30 children (in the sample) who have serious food allergies. [3 marks]

d. If the sample size is increased what will happen to the probability in part (c), will it increase, decrease, or stay the same? Explain your answer without any calculation or formula. [2 marks]