The images you uploaded show a statistics problem related to airline overbooking. Here’s a quick breakdown of the problem and its solution:

Problem Context:

• Airline Booking: 170 seats available, but 181 passengers are booked because 14% typically do not show up.
• You are asked to compute the expected number of passengers who show up, the standard deviation, and the probability that specific seat scenarios occur.

Part (a): Expected number of passengers who show up and standard deviation:

• Expectation: Out of 181 passengers booked, the airline expects a certain number to show up, given that each has a 14% chance of not showing up (or 86% of showing up).
  • $E(X) = n \times p = 181 \times 0.86 = 155.66$
• Standard Deviation:
  • $\sigma(X) = \sqrt{n \times p \times (1-p)} = \sqrt{181 \times 0.86 \times 0.14} = 4.67$

Part (b): Probability that 5 seats will be empty:

• This uses the binomial distribution to calculate the probability that exactly 5 out of 170 seats will be empty.
  • $P(5 \text{ seats empty}) = 0.0109$

Part (c): Probability that a passenger is denied boarding due to overbooking:

• Given 181 passengers and only 170 seats, the probability that overbooking causes a passenger to be denied boarding is very low, calculated as:
  • $P(\text{overbooking issue}) = 0.0002$

Would you like a more detailed breakdown of any of these parts or clarifications? Here are some related questions to consider:

1. How is the binomial distribution applied to overbooking problems in real-life scenarios?
2. What factors might change the expectation of passengers showing up (e.g., weather, time of year)?
3. How can airlines minimize the risk of overbooking issues while still optimizing seat usage?
4. How could you use standard deviation to plan for fluctuations in passenger turnout?
5. What other probability distributions might be relevant in analyzing overbooking?

Tip: The binomial distribution is ideal for yes/no events like "does the passenger show up?" because it models independent trials with two outcomes, making it perfect for this kind of scenario.