In a certain city, the average monthly temperature is 30 degrees Celsius with a standard deviation of 3 degrees. What is the probability that the average temperature for a randomly selected month falls between 27 and 33 degrees?

Step 1 ：First, we need to convert the temperature values to z-scores. The z-score is calculated using the formula: $z=\frac{X-\mu }{\sigma }$, where X is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step 2 ：For X = 27, the z-score is: $z=\frac{27-30}{3}=-1$

Step 3 ：For X = 33, the z-score is: $z=\frac{33-30}{3}=1$

Step 4 ：Next, we find the probabilities associated with these z-scores from the standard normal distribution table. The probability for z = -1 is 0.1587 and for z = 1 is 0.8413.

Step 5 ：To find the probability that a randomly selected score falls between these two z-scores, subtract the smaller probability from the larger one: $0.8413-0.1587=0.6826$