Answer:
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).