Question

Suppose that x represents the loading time for a truck at the ship's loading dock. If the mean loading time is 15 minutes, find the appropriate probability density function for x.

a) 0 for x<0 and 1/15 for 0≤x≤15, 0 for x>15
b) 1/151/15 for 0≤x≤15, 0 for x<0 and x>15
c) 0 for x<0 and 1/15 for 015
d) 1/15 for 015

Answer 1

The appropriate probability density function is f(x) = 1/15 for 0≤x≤15, with a probability of 0 for times outside that range.

Step-by-step explanation:

If a truck's loading time, x, at a ship's loading dock has a mean loading time of 15 minutes and is uniformly distributed between 0 and 15 minutes, the appropriate probability density function for x would be as follows:

f(x) = 1/15 for 0≤x≤15, 0 for x<0 and x>15.

This indicates that for any given time interval within the 0 to 15 minutes range, the probability of the truck's loading time falling within that interval is the same and is given by the density of 1/15 for each minute. The probability is 0 for any time outside that interval, meaning it's impossible for the loading time to be less than 0 or greater than 15 minutes in this scenario.