3. The drying times of paint can be assumed to be normally distributed. A paint manufacturer paints 10 test areas with a new paint. The following drying times, to the nearest minute, were recorded.
$$82 , \quad 98 , \quad 140 , \quad 110 , \quad 90 , \quad 125 , \quad 150 , \quad 130 , \quad 70 , \quad 110 .$$
- Calculate unbiased estimates for the mean and the variance of the population of drying times of this paint.
Given that the population standard deviation is 25 ,
- find a 95\% confidence interval for the mean drying time of this paint.
Fifteen similar sets of tests are done and the \(95 \%\) confidence interval is determined for each set.
- Estimate the expected number of these 15 intervals that will enclose the true value of the population mean \(\mu\).