A game is played with a spinner on a circle, like the minute hand on a clock. The circle is marked evenly from 0 to 100, so, for example, the 3:00 position corresponds to 25, the 6:00 position to 50, and so on. The player spins the spinner, and the resulting number is the number of seconds he or she is given to solve a word puzzle. Let X = amount of time the player is given to solve the puzzle.

a. Explain how you know that X is a uniform random variable.

b. Write down the density function for X. Be sure to specify the range of values for which it holds.

c. Find P(X ≤ 15 seconds).

d. Find P(X ≥ 40 seconds).

e. Draw a picture of the density function of X, and use it to illustrate the probabilities that you found in parts (c) and (d).

f. What is the expected value of X? This was not covered in the text, so explain your reasoning.