4. A fair die is rolled 150 times. What is the probability of a 6 coming up between 20 and 30 times? (20 times or 30 times would count.)

We could do this by constructing the probability distribution as in the previous problem, but that would take so much effort that it would be worthwhile to use the normal approximation to the binomial distribution.

The number of times the experiment is repeated is

The probability of success each time is

The mean is

np = 150(1/6) = 25

and the standard deviation is

Since we are counting the 20 and the 30, the upper limit is 30.5 and the lower limit is 19.5.

We convert these numbers to z-scores using the formula