In a hotel chain, the mean number of rooms is 98 with a standard deviation of 4 rooms. Use the empirical rule to find the probability that a randomly chosen hotel will have more than 102 rooms.
The probability that the randomly chosen hotel has more than 102 rooms is

Step 1 ：Given that the mean number of rooms in the hotel chain is 98 and the standard deviation is 4.

Step 2 ：The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, almost all data will fall within three standard deviations of the mean. Specifically, 68% of data falls within the first standard deviation, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 3 ：A hotel with more than 102 rooms is more than one standard deviation away from the mean. According to the empirical rule, the probability that a randomly chosen hotel will have more than 102 rooms is the probability that it falls more than one standard deviation above the mean.

Step 4 ：To find this, we can subtract the probability that a hotel falls within one standard deviation of the mean (68%) from 100%. This will give us the probability that a hotel falls more than one standard deviation away from the mean, either above or below.

Step 5 ：Since we're only interested in hotels with more than 102 rooms (i.e., more than one standard deviation above the mean), we divide this result by 2.

Step 6 ：\(mean = 98\)

Step 7 ：\(std\_dev = 4\)

Step 8 ：\(one\_std\_dev\_above = 102\)

Step 9 ：\(prob\_within\_one\_std\_dev = 68\)

Step 10 ：\(prob\_more\_than\_one\_std\_dev = 100 - prob\_within\_one\_std\_dev = 32\)

Step 11 ：\(prob\_more\_than\_102\_rooms = prob\_more\_than\_one\_std\_dev / 2 = 16.0\)

Step 12 ：Final Answer: The probability that a randomly chosen hotel will have more than 102 rooms is \(\boxed{16\%}\).