Question

The response time of a fire department in an emergency call is the period between the time the call is received by the dispatcher and the time the first truck service arrives on the scene. It was found that the response time follows a normal distribution with mean of 10 min and standard deviation of 3 min. What is the probability that the response time is exactly equal to 17.5 min?

Answer 1

The probability of a continuous variable like response time being exactly a specific value in a normal distribution is zero because the area under the curve at a single point is zero.

Step-by-step explanation:

In the context of probabilities associated with normal distributions, the probability of observing a variable that takes on an exact value is essentially zero. This is because the normal distribution is continuous and the area under the curve at a single point is 0. To find probabilities for continuous random variables like response times, we look for the probability that the response time falls within an interval rather than being exactly a certain value.