Question

The random variable € is known to be uniformly distributed between 10 and 35. Which of the following graphs accurately represents this probability density function?

10 15 20 25 30 35 40 45

Select your answer.

a. Compute P(c < 23.5) (to 2 decimals).

b. Compute P(13 < € < 32) (to 2 decimals): Enter negative value as negative number.

c. Compute E(c) (to 1 decimal place if necessary).

Answer 1

The probability density function (pdf) for a continuous uniform distribution between 10 and 35 is a rectangle. For P(c < 23.5), the area under the curve is 0.46. For P(13 < € < 32), the area under the curve is 0.76. The expected value of the distribution is 22.5.

Step-by-step explanation:

The probability density function (pdf) for a continuous uniform distribution between 10 and 35 is a rectangle with a height of 1/25 and a base of 25. The graph that accurately represents this probability density function is a rectangle with the vertical sides at y = 0 and y = 1/25, and the horizontal sides at x = 10 and x = 35.

1. a. To compute P(c < 23.5), we need to find the area under the probability density function curve between 23.5 and 35. Since the probability density function is a rectangle, the area is equal to the height (1/25) multiplied by the width (11.5). Therefore, P(c < 23.5) = 1/25 * 11.5 = 0.46 (rounded to 2 decimals).
2. b. To compute P(13 < € < 32), we need to find the area under the probability density function curve between 13 and 32. Since the probability density function is a rectangle, the area is equal to the height (1/25) multiplied by the width (19). Therefore, P(13 < € < 32) = 1/25 * 19 = 0.76 (rounded to 2 decimals).
3. c. To compute E(c), we use the formula for the expected value of a continuous uniform distribution, which is (a + b) / 2. In this case, a = 10 and b = 35. Therefore, E(c) = (10 + 35) / 2 = 22.5 (rounded to 1 decimal).