Question

IGNORE WORK ON PAPER PLS HELP

3. A game at an arcade consists of a balloon that is inflated little-by-little during each round of play. The player wins. when the balloon pops. The amount of air (in cubic inches) that is needed to make the balloon pop can be modeled by a uniform distribution on the interval from 25 to 35 cubic inches of air.

(a) Draw a density curve to model the amount of air that is needed to make the balloon pop. Be sure to include scales on both axes.

(b) About what percent of the time will the balloon pop upon receiving at most 28 cubic inches of air?

(c) Find the first quartile (Q1) of this distribution.


4. The manager of the arcade wants to know how quickly players switch from one game to another. After conducting a
study, he concludes that the amount of time that people spend playing a game before switching to a different game can be modeled by a normal distribution with mean 2.1 minutes and standard deviation 0.4 minutes.
Sketch the normal density curve. Label the mean and the points that are 1, 2, and 3 standard deviations from the mean.

Answer 1

(a) To draw a density curve for the uniform distribution on the interval from 25 to 35 cubic inches of air, you can use a horizontal line segment that represents a constant density over that interval. The density should be 1 divided by the width of the interval, which is 35 - 25 = 10 cubic inches. Here's how you can represent it graphically