The arrival time of an elevator in a 12-story dormitory is equally likely at any time during the next 4 minutes. a. Calculate the expected arrival time. Note: Round your answer to 2 decimal places. Expected arrival time square b. What is the probability that an elevator arrives in less than 11/2 minutes? Note: Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places. Probability square c. What is the probability that the wait for an elevator is more than 11/2 minutes? Note: Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places. Probability square

1. Calculate the expected arrival time For a uniform distribution over , the expected value is the midpoint. **Expected Value = \frac{a + b}{2}** where and . So, .2. Calculate probability for arrival in less than minutes Convert to decimal: . Probability is area under the curve from to . Since , it covers the entire interval. **Probability = \frac{\text{Length of Interval}}{\text{Total Length}} = \frac{4}{4} = 1**.3. Calculate probability for wait more than minutes Since exceeds the interval , probability is zero. **Probability = \frac{\text{Length of Interval beyond 4}}{\text{Total Length}} = \frac{0}{4} = 0**.