A cordless drill has several torque settings for driving different screws into different materials. A manufacturer models the torque setting required for a randomly selected task with a probability...

A cordless drill has several torque settings for driving different screws into different materials. A manufacturer models the torque setting required for a randomly selected task with a probability distribution given by

a. Verify that this is a valid probability distribution.

b. Find the mean, variance, and standard deviation of X.

c. A torque setting is classified as rare if it is more than one standard deviation from the mean. Find the probability of a task requiring a rare torque setting.