To solve this problem, we will first determine the mean and standard deviation of the distribution of sample proportion.
The mean of the distribution of sample proportion is equal to the population proportion, which is 0.75.
The standard deviation of the distribution of sample proportion is given by:
σ = sqrt[ (p * (1 - p)) / n ]
where p is the population proportion (0.75), and n is the sample size (60).
σ = sqrt[ (0.75 * (1 - 0.75)) / 60 ]
= 0.0625
To find the probability that more than 80% of the sample flights are on time, we will use a z-score calculation.
z = (x - μ) / σ
where x is the value we want to find the probability of, μ is the mean of the distribution (0.75), and σ is the standard deviation of the distribution (0.0625).
z = (0.8 - 0.75) / 0.0625
= 0.8
Using a standard normal table or calculator, we can find that the probability of a z-score of 0.8 or higher is approximately 0.2119.
Therefore, the probability that more than 80% of the sample flights are on time is approximately 0.2119.