An airliner carries 400 passengers and has doors with a height of 78 in. heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 in. if a male passenger is randomly selected, find the probability that he can fit through the doorway without bending

The probability would be 0.9993.

We find the z-score that corresponds with this situation.  Z-scores are found using the formula:



Using our information we have:


Using a z-table (http://www.z-table.com), we look up the corresponding z-score for this.  This gives us the area to the left of the score, so the heights that are less than 78 inches.  This gives us the probability 0.9993.

C. 40,320 just did the math right now