Question

1. At a particular amusement park, most of the live characters have height requirements of a minimum of 57 in. and a maximum of 63 in. A survey found that​ women's heights are normally distributed with a mean of 62.4 in. and a standard deviation of 3.6 in. The survey also found that​ men's heights are normally distributed with a mean of 68.3 in. and a standard deviation of 3.6 in.
Find the percentage of men meeting the height requirement.  
The percentage of men who meet the height requirement is___?___ .
​(Round answer to nearest hundredth of a percent - i.e. 23.34%).

2. An elevator has a placard stating that the maximum capacity is 2280 lb or 15 passengers.​ This means that if the elevator was filled with 15 adult male passengers, their mean weight could be up to 2280/15 = 152 pounds.

If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 152 lb.​ (Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 31 lb​.)
The probability the elevator is overloaded is ___?___.
​(Round answer to nearest hundredth of a percent - i.e. 23.34%)

Answer 1