Questions: Tammy is a biologist studying a species of snake native to only an isolated island. She selects a random sample of 8 of the snakes and records their body lengths (in meters) as listed below. 4.9, 5.3, 2.5, 4.6, 5.2, 3.8, 5.1, 5.0 (a) Graph the normal quantile plot for the data. To help get the points on this plot, enter the data into the table in the correct order for a normal quantile plot. Then select "Compute" to see the corresponding area and z-score for each data value.

Solution Steps

First, we need to order the data in ascending order: \[ 2.5, 3.8, 4.6, 4.9, 5.0, 5.1, 5.2, 5.3 \]

Next, we compute the quantiles for each data point. For a sample size of \( n = 8 \), the quantiles are: \[ \frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8} \] which simplifies to: \[ 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0 \]

Using the standard normal distribution, we find the z-scores corresponding to these quantiles: \[ \begin{align_} z(0.125) & \approx -1.1503 \\ z(0.25) & \approx -0.6745 \\ z(0.375) & \approx -0.3186 \\ z(0.5) & = 0 \\ z(0.625) & \approx 0.3186 \\ z(0.75) & \approx 0.6745 \\ z(0.875) & \approx 1.1503 \\ z(1.0) & \approx \infty \quad (\text{not used}) \end{align_} \]

We pair each ordered data point with its corresponding z-score: \[ \begin{align_} (2.5, -1.1503) \\ (3.8, -0.6745) \\ (4.6, -0.3186) \\ (4.9, 0) \\ (5.0, 0.3186) \\ (5.1, 0.6745) \\ (5.2, 1.1503) \\ (5.3, \infty) \quad (\text{not used}) \end{align_} \]

Final Answer