ONLY A OR B PART

A medical report mentioned that 28% of children aged under 6 years old in Hong Kong had a good diet. (a) A nutritionist, Dr Lam randomly selected 250 children aged under 6 years old in Hong Kong. Find the probability that the sample proportion of the selected children under 6 years old in Hong Kong having a good diet would exceed 31%. Correct the final answer to 4 decimal places. (b) A nutritionist, Dr Chan randomly selected 200 children aged under 6 years old in Hong Kong. By using the continuity correction method, find the probability that at most 50 of the selected children aged under 6 years old in Hong Kong having a good diet. Correct the final answer to 4 decimal places. (c) A nutritionist, Dr Wong randomly selected 500 children aged under 6 years old in Hong Kong and 95 of them had a good diet. He claims that the true proportion of children aged under 6 years old in Hong Kong having a good diet is decreased. Test his claim by using critical value approach at 0.05 level of significance. Correct the test statistic to 2 decimal places