1. Sketch the normal curve for the variable.
2. Shade the region of interest and mark its delimiting x-value(s).
3. Find the z-score(s) for the value(s).
4. Use an applet (or the pnorm command in R) to find the associated area.

Find the proportion of SAT-takers who score between 1150 and 1300. Assume that SAT scores are approximately normally distributed with mean \(\mu=1100\) and standard deviation \(\sigma = 200\).

Rossman and Chance Normal Probability Calculator

We can also find the observation associated with a percentage/proportion.

Recall: The \(w\)th percentile \(p_w\) is the observation that is higher than w% of all observations \[P(X < p_w) = w\]

1. Sketch the normal curve for the variable.
2. Shade the region of interest and label the area.
3. Use the applet (or R - see below) to determine the z-score for the area.
4. Find the x-value using \(z\), \(\mu\), and \(\sigma\).

Note that if \(z = \frac{x-\mu}{\sigma}\), then \(x = \mu + z\sigma\).

SAT scores are approximately Normal(\(\mu=1100\), \(\sigma=200\)). Find the 90th percentile for SAT scores.

Rossman and Chance Normal Probability Calculator