An airliner carries 300 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. Complete parts (a) through (d 4 of 1 a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending The probability is \( \square \) (Round to four decimal places as needed)

To determine the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the proportion of men who are 70 inches tall or shorter. Given that men's heights are normally distributed, we can calculate this by converting the height to a z-score. 1. **Calculating the Z-Score:** \[ Z = \frac{X - \mu}{\sigma} = \frac{70 - 69}{2.8} \approx 0.3571 \] 2. **Finding the Probability:** Now, we need to look up the z-score of 0.3571 in the standard normal distribution table or use a calculator. This gives us a probability of approximately 0.6401. Thus, the probability that a randomly selected male passenger can fit through the doorway without bending is **0.6401** (rounded to four decimal places).