Answer all the following questions regarding confidence intervals.

2.1. Find the confidence interval of the sample mean of a random variable ofsample size 25 if the population standard deviation is 2 and the sample mean is 8. Find a 99% confidence interval for the population true mean.

2.2. Find the 90% confidence interval estimate of the true population mean income if a sample of 169 families gives a sample mean of $30,500. From previous experience we know that the population standard deviation is $6,000.

2.3. A simple random sample of 25 a particular species of newts and measure their tails. The mean tail length of our sample is 5 cm.

a.) If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 95% confidence interval for the mean tail length of all newts in the population?

b.) If we know that0.2cm is the standard deviation of the tail lengths of all newts in the population, then what is a 99% confidence interval for the mean tail length of all newts in the population?