An airliner carries 100 passengers and has doors with a height of 70 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in.    a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending. The probability is 0.6406.   b. If half of the 100 passengers are​ men, find the probability that the mean height of the 50 men is less than 70 in.   The probability is _____-. ​(Round to four decimal places as​ needed.)

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An airliner carries 100 passengers and has doors with a height of
70 in. Heights of men are normally distributed with a mean of 69.0
in and a standard deviation of 2.8 in. 
 
a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending. The probability is 0.6406.
 
b. If half of the 100 passengers are​ men, find the probability that the mean height of the 50 men is less than 70 in.
 
The probability is _____-.
​(Round to four decimal places as​ needed.)
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