Solved Problems

The compressive strength of concrete samples is normally distributed with $\mu = 4000$ psi and $\sigma = 200$ psi. What is the probability that a sample has a strength less than 3800 psi?

Using the same parameters as Problem 1 ($\mu = 4000$ psi, $\sigma = 200$ psi), what is the probability that a sample's strength falls between 3900 psi and 4300 psi?

The time between failures of a pump follows an exponential distribution with a mean time to failure ($\theta$) of 500 hours. What is the probability that the pump survives at least 600 hours before failing?

A structural engineer needs to take measurements on a bridge. A specialized piece of equipment is scheduled to arrive randomly between 8:00 AM and 10:00 AM. The time of arrival follows a continuous uniform distribution. If the engineer starts waiting at 8:30 AM, what is the probability they will wait more than 45 minutes for the equipment to arrive?