1. Suppose a population unkown population mean and population standard deviation \(2.5\). A sample of \(450\) observations has a sample mean of \(\bar{x}=62\). Find a \(95 \%\) confidence interval.

  2. What are the \(z\)-scores corresponding to a \(70 \%\) confidence level?

  3. Suppose average pizza delivery times are normally distributed with an unknown population mean and a population standard deviation of six minutes. A random sample of \(28\) pizza delivery restaurants is taken and has a sample mean delivery time of \(36\) minutes. Find a \(90 \%\) confidence interval for the population mean delivery time.

  4. From a population with population mean \(16\) and standard deviation \(2\) a sample of \(35\) observations is taken. Provide an interval such that there is an \(80 %\) chance that the sample mean falls within the range.

  5. Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of \(3\) points. A random sample of \(36\) scores is taken with an mean score of \(72\). Find a \(98 \%\) confidence interval for the mean exam score of the population.