Final answer:
The height of the rectangle in the density curve that represents temperatures between 0°F and 40°F is found by ensuring that the total area under the curve equals 1. Given the width is 40°F, the height is calculated to be 0.025.
Step-by-step explanation:
The student has asked for the height of a rectangle in a density curve representing all possible temperatures between 0°F and 40°F. In a density curve, the entire area under the curve must equal 1, as this represents the entire probability of all outcomes in a uniform distribution.
Given the width of the rectangle is 40°F (from 0°F to 40°F), to find the height, we use the formula for the area of a rectangle, which is Area = Height × Width.
Knowing the area must equal 1, as this is a probability density function, we can set up the equation 1 = Height × 40.
To solve for the height, we divide both sides by 40, yielding a height of 0.025.