3. A random variable \(X\) is distributed normally with a standard deviation of 6.8
Sixty observations of \(X\) are made and found to have a mean of 31.4
- Find a 90\% confidence interval for the mean of \(X\).
- How many observations of \(X\) would be needed in order to obtain a \(90 \%\) confidence interval for the mean of \(X\) with a width of less than 1.5
(5 marks)