According to a flight statistics website, in 2009, a certain airline had the highest percentage of on-time flights in the airlines industry, which was 81.2%. Assume this percentage still holds true for that airline. Use the normal approximation to the binomial distribution to complete parts a through c below.
Determine the probability that, of the next 30 flights from this airline, less than 24 flights will arrive on time.
The following information about the Binomial distribution is provided:
The population proportion of success is , and the sample size is . We need to compute
The population mean is computed as:
and the population standard deviation is computed as:
Therefore, we get that
so then, we conclude that , which ends the calculation of the requested probability
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