The random variable XXX is normally distributed with unknown mean μ\muμ and known variance σ2\sigma^2σ2. A random sample of 16 observations of XXX produced a 95%95\%95% confidence interval for μ\muμ of (40.04,43.96)(40.04, 43.96)(40.04,43.96).
Find the mean of the sample.
Show that the standard deviation σ\sigmaσ is 4.
The a%a \%a% confidence interval using the 16 observations has a width of 3.3.
Calculate the value of aaa.
Find the smallest sample size, of observations from XXX, that would be required to obtain a 95%95\%95% confidence interval for μ\muμ of width at most 2.5.
