Question

Jackson goes to the gym 0,2 or 3 days in a week, depending on work demands at the office. The probability that he goes 0 days is 0.1, the probability that he goes 2

days is 0.65, and the probability that he goes 3 days is 0.25. What is the expected value of the number of days per week for which Jackson goes to the gym?
A. 1.55
B. 2.05
C. 2.15
D. 2.50
E. 2.76

Answer 1

The expected number of days per week Jackson goes to the gym is calculated using the probabilities for 0, 2, and 3 days. By multiplying each number of days by its probability and summing these, we find the expected value is 2.05, corresponding to option B.

Step-by-step explanation:

The student is asking for the expected value for the number of days Jackson goes to the gym given certain probabilities for going 0, 2, or 3 days per week. The expected value (EV) is calculated by multiplying each outcome by its probability and summing these products.

To calculate the expected number of days Jackson goes to the gym, we use the formula for expected value:

• EV = (0 days × P(0 days)) + (2 days × P(2 days)) + (3 days × P(3 days))

P(0 days) is 0.1, P(2 days) is 0.65, and P(3 days) is 0.25:

• EV = (0 × 0.1) + (2 × 0.65) + (3 × 0.25)
• EV = (0) + (1.3) + (0.75)
• EV = 2.05

Therefore, the expected number of days per week Jackson goes to the gym is 2.05, which corresponds to option B.