4.) The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 20 and B = 50. What is the probability that preparation is within 2 minutes of the mean time?

And using the cumulative distribution function we got:

The probability that preparation is within 2 minutes of the mean time is 0.134

Step-by-step explanation:

For this case we define the following random variable X= (minutes) for a lab assistant to prepare the equipment for a certain experiment , and the distribution for X is given by:

The cumulative distribution function is given by:

The expected value is given by:

And we want to find the following probability:

And we can find this probability on this way:

And using the cumulative distribution function we got:

The probability that preparation is within 2 minutes of the mean time is 0.134