Calculation of probability based on normal distribution

1. The length of time a customer must wait in line at the post office has approximately a normal distributionwith a meanof 5.8 minutes and a standard deviationof 2.6 minutes. Find the probabilitythat the customer will wait between 4 and 8 minutes.

2. The lifetime of a certain brand of tire follows an approximately normal distribution with a mean of 30,000 miles and a standard deviation of 4000 miles. The probability that a tire of this brand will last between 31,000 and 36,000 miles is?

The solution gives the details of calculation probability of events based on Z score and normal distribution.