4 A continuous random variable is normally distributed with mean \(\mu\). A significance test for \(\mu\) is carried out, at the \(5 \%\) significance level, on 90 independent occasions.
- Given that the null hypothesis is correct on all 90 occasions, use a suitable approximation to find the probability that on 6 or fewer occasions the test results in a Type I error. Justify your approximation.
- Given instead that on all 90 occasions the probability of a Type II error is 0.35 , use a suitable approximation to find the probability that on fewer than 29 occasions the test results in a Type II error.