Final answer:
The average number of airplanes arriving and departing from an airport per hour is 200 planes, which follows a normal distribution with a mean of 200 and a standard deviation of 60. The probability of exactly 100 arrivals and departures is zero for a continuous distribution. However, the probability of at most 100 arrivals and departures can be calculated using the Z-score and a standard normal distribution table or a statistical calculator.
Step-by-step explanation:
When dealing with the number of take-offs and landings at an airport, we're considering a normal distribution where the mean (μ) is 200 planes and the standard deviation (σ) is 60 planes. To find various probabilities related to this distribution, we would typically use a standard normal distribution table (Z-table) or a statistical calculator capable of computing normal probabilities.
a. Number of airplanes per hour
The average number of airplanes arriving and departing from the airport per hour is 200 planes.
b. Probability of exactly 100 arrivals and departures
The probability of exactly 100 arrivals and departures is not directly calculable because the normal distribution is continuous, so the probability of any single exact value is technically 0. However, we can calculate the probability of a narrow range around 100 using a normal probability calculator.
c. Probability of at most 100 arrivals and departures
To determine the probability of at most 100 arrivals and departures, we would calculate the cumulative probability up to and including 100 using the normal distribution. This involves finding the Z-score for 100 and then looking up the corresponding cumulative probability in the Z-table or using a statistical calculator.