A Study of the Ability of Individuals to Walk in a Straight

A study of the ability of individuals to walk in a straight line reported that accompanying data on cadence (strides per seconds) for a sample of n - 20 randomly selected healthy men: $$\begin{array} { l l l l l l l l l l } .95 & .81 & .93 & .95 & .93 & .86 & 1.05 & .92 & .85 & .81 \\.92 & .96 & .92 & 1.00 & .78 & 1.06 & 1.06 & .96 & .85 & .92\end{array}$$ A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from MINITAB follows. $$\begin{array} { l l l l l c } \text { Variable } & N & \text { Mean } & \text { Median } & \text { StDev } & \text { SEMean } \\\text { Cadence } & 20 & 0.9255 & 0.9300 & 0.0809 & 0.0181\end{array}$$
a. Calculate and interpret a 95% confidence interval for a population mean cadence.
b. Calculate and interpret a 95% prediction interval for the cadence of a single individual randomly selected from this population.
c. Calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%.