The time required to finish a test in normally distributed with a mean of 40 minutes and a standard deviation of 8 minutes. what is the probability that a student chosen at random will finish the test in between 32 and 56 minutes?

Notice that 32=40-8, and 56 = 40+16 = 40+2*8.

This is important because then you know it is the area between -1 sigma and 2 sigma.

The area between -1 sigma and 0 is 34.1%, the area between 0 and 2 sigma is 47.7 %, the total is = 81.8%

The answer is p = 81.8% or 0.818 depending on how your teacher prefers to write down a probability with or without %. Most find both fine.

Where are the following equations?