Sunita has a six-sided die with faces marked 1, 2, 3, 4, 5, 6. The probability of a six on any throw is \(p\). She throws the die 500 times and obtains 70 sixes.

(a) Calculate an approximate 99% confidence interval for \(p\). [4]

(b) Sunita believes that the die is fair. Use your answer to part (a) to comment on her belief. [1]

Sunita uses the result of her 500 throws to calculate an \(\alpha\%\) confidence interval for \(p\). The interval has width 0.04.

(c) Find \(\alpha\). [5]