Question

On a particular airline, 65% of all passengers accept a bag of peanuts during their flight. The airplanes for this airline have 180 seats, and all seats are always sold out. (Use this for #3 – 5).

5. Would bringing 126 bags of peanuts be sufficient on each flight? Calculate the probability that they would run out of peanuts on a randomly chosen flight, making sure to sketch, label, and shade the Standard Normal Distribution appropriately.

Answer 1

The number of passengers out of the 180 seats who accept bag of peanuts could be modelled here as:

This is approximated to a normal distribution here as:

The probability here required is:
P(X > 126)

Applying the continuity correction, we have here:
P(X > 126.5)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

therefore 0.0694 is the required probability here.

This is shown in the standard normal plot as: