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.