Section 9.9 Exercises
Checkpoint 9.9.1. - Computing basic standard normal probabilities.
Compute
- \begin{equation*} P( Z \gt 0) \end{equation*}
- \begin{equation*} P( Z \lt 0.892) \end{equation*}
- \begin{equation*} P( Z \lt -0.892) \end{equation*}
- \begin{equation*} P( -1.45 \lt Z \lt 2.37) \end{equation*}
-
\begin{equation*} P( -1 \lt Z \lt 1) \end{equation*}which is the probability of lying within 1 standard deviation of the mean.
-
\begin{equation*} P( -2 \lt Z \lt 2) \end{equation*}which is the probability of lying within 2 standard deviations of the mean.
-
\begin{equation*} P( -3 \lt Z \lt 3) \end{equation*}which is the probability of lying within 3 standard deviations of the mean.
- A value for a so that\begin{equation*} P( Z \lt a) = 0.8 \end{equation*}which would be the location of the 80th percentile.
Checkpoint 9.9.2. - Computing basic normal probabilities.
Given \(\mu = 25\) and \(\sigma = 4\) compute
\begin{equation*}
P(X \lt \mu)
\end{equation*}
\begin{equation*}
P( X \gt 26)
\end{equation*}
\begin{equation*}
P( X \gt 22)
\end{equation*}
\begin{equation*}
P( 20 \le X \le 26)
\end{equation*}
Checkpoint 9.9.3. - IQ values.
The Intelligence Quotient (IQ) is a measure of your ability to think and reason. Presuming that IQ scores are normally distributed with mean 100 and standard deviation 15, determine the location of the 90th percentile. That is, the IQ score below which you will find approximately 90% of other IQ scores.