5 Sunita has a six-sided die with faces marked \(1,2,3,4,5,6\). The probability that the die shows a six on any throw is \(p\). Sunita throws the die 500 times and finds that it shows a six 70 times.
- Calculate an approximate \(99 \%\) confidence interval for \(p\).
- Sunita believes that the die is fair. Use your answer to part (a) to comment on her belief.
- Sunita uses the result of her 500 throws to calculate an \(\alpha \%\) confidence interval for \(p\). This interval has width 0.04 .
Find the value of \(\alpha\).