Question

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Part 1
The graph to the right is the uniform density function for a friend who is x minutes late. Find the probability that the friend is at least 23 minutes late. What is the probability? Out of 30 mins.

Answer 1

The question describes a uniform density function, which means that the probability is constant for any given time interval within the given range. The provided range is 0 to 30 minutes.

Let's denote the uniform density function as f(x) for x being the time in minutes late. We are asked to find the probability that a friend is at least 23 minutes late, which means we need to find the area under the density function from x = 23 to x = 30.

Since it's a uniform distribution, we can calculate the probability by finding the length of the interval (30 - 23) and dividing it by the total length of the range (30 - 0).

Probability = (Length of interval) / (Total length of range)

Probability = (30 - 23) / (30 - 0)

Probability = 7 / 30

The probability that the friend is at least 23 minutes late is 7/30 or approximately 0.2333 (rounded to four decimal places).