Uniform, Normal and Exponential Distributions and Conditional Probability

1. The length of time it takes to find a parking spot, during the summer terms on a campus, follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. The probability that a student, attending classes during the summer terms, will find a parking spot in less than 3 minutes is

2. Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete the quiz is uniformly distributed over the interval [0, 15]. Suppose a student from the class is selected at random, what is the probability that the student will take more than 10 minutes to complete the quiz?

3. The defective rate for a certain electronic component is known to be 6%. If 100 of the components are selected at random, what is the probability that less than 10 are defective?

4. A rock crushing company has three plants, all receiving blasted rocks in bulk. The amount of rocks that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume that the plants operate independently of each other. What is the probability that two of the plants will crush more than 4 tons on a given day?

5. Suppose that the life of an electronic component has an exponential distribution with a mean life of 500 hours. Suppose that the component was in operation for 400 hours. What is the conditional probability that it will last another 500 hours?

6. Suppose that an e-business on the Internet receives an average of 5 orders per hour. Assume that the number of orders follows a Poisson process. What is the probability that up to one hour will elapse until two orders are received?

7. The value of zo such that is

See attached file for full problem description.