At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied. Assume each flight is independent of the others. Find the probability that eight or more of the flights will arrive on time.

The probability that eight or more of the flights will arrive on time is 0.5256

Probabilities are used to determine the chances of events

The given parameters are:

The required probability is then represented as:

This is calculated using the following binomial probability formula

So, we have:

This gives

This gives

Hence, the probability is 0.5256

Read more about probabilities at:

link

52.56% probability that eight or more of the flights will arrive on time.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it is on time, or it is not. The probability of a flight being on time is independent from other flights. So we use the binomial probability distribution to solve this question.]

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

At a certain airport, 75% of the flights arrive on time.

This means that

A sample of 10 flights is studied.

This means that

Find the probability that eight or more of the flights will arrive on time.

In which

52.56% probability that eight or more of the flights will arrive on time.