Question

1. quick, click! the density curve models the amount of time the subject has to wait for the light to flash during a reaction time test. what height must the density curve have? about what proportion of the time will the light turn on between 2.75 and 4.25 seconds?

height is $\frac{1}{3}$

the empirical rule

1. long jump at a major track meet, the official recorded the distance, to the nearest centimeter, of each athletes best jump. use the empirical rule to determine if the distribution is normal.

Explanation:

Problem 5

Step1: Find density curve height

The curve is uniform from 2 to 5 seconds. Area under curve = 1: height × (5-2) = 1 → height = $\frac{1}{3}$.

Step2: Calculate proportion between 2.75 & 4.25

Width = 4.25 - 2.75 = 1.5. Proportion = height × width = $\frac{1}{3}×1.5 = 0.5$.

The empirical rule requires ~68% within mean±1SD, ~95% within mean±2SD, ~99.7% within mean±3SD. Mean=577.3, SD=4.713:

• Mean±1SD: 577.3±4.713 ≈ 572.6-582.0. Most data (histogram peak at 575, Q1=574.5, Q3=581.5) lies here, matching ~68%.
• Mean±2SD: 577.3±9.426 ≈567.9-586.7. Min=564 (slightly below), Max=586 (within), close to ~95%.
• The histogram is roughly symmetric, centered at the mean.

Answer:

Height: $\frac{1}{3}$; Proportion: 0.5

Problem 6