An amusement park is considering the construction of an artificial cave to attract visitors. The proposed cave can only accommodate 36 visitors at one time. In order to give everyone a realistic feeling of the cave experience, the entire length of the cave would be chosen such that guests can barely stand upright for 98% of the all the visitors.

The mean height of American men is 70 inches with a standard deviation of 2.5 inches. An amusement park consultant proposed a height of the cave based on the 36-guest-at-a-time capacity. Construction will commence very soon.

The park CEO has a second thought at the last minute, and asks yours truly if the proposed height is appropriate. What would be the proposed height of the amusement park consultant? And do you think that it is a good recommendation? If not, what should be the appropriate height? Why?