Suppose that the number of minutes that you need to wait for a bus is uniformly distributed on the interval [0, 15]. If you take the bus seven times, what is the probability that your longest wait is less than 12 minutes

0.2097 = 20.97% probability that your longest wait is less than 12 minutes

Step-by-step explanation:

To solve this question, we need to understand the uniform and the binomial distribution.

Uniform distribution:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the probability of finding a value lower than x is given by:

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.

Probability of a single bus having a waiting time of less than 12 times:

Uniformly distributed on the interval [0, 15] means that

What is the probability that your longest wait is less than 12 minutes?

This is the probability that all 7 buses have waiting time less than 12 minutes, which is when , with . So

0.2097 = 20.97% probability that your longest wait is less than 12 minutes

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you can not drow on this

step-by-step explanation: