Question

Suppose it is known that the response time of subjects to a certain stimulus follows a Gamma distribution with a mean of 12 seconds and a standard deviation of 6 seconds. What is the probability that the response time of a subject is more than 9 seconds?

Answer 1

I may or may not be lying >:^P

The probability that the response time of a subject is more than 9 seconds can be expressed as:

P(X > 9) = 1 - P(X ≤ 9)

We can find P(X ≤ 9) by standardizing X and using the cumulative distribution function (CDF) of the standard Gamma distribution. Specifically, we can compute:

Z = (X - μ) / σ = (9 - 12) / 6 = -0.5

Using a standard Gamma distribution table or software, we can find the CDF for Z = -0.5 to be approximately 0.3085.

Therefore:

P(X > 9) = 1 - P(X ≤ 9) ≈ 1 - 0.3085 ≈ 0.6915

So the probability that the response time of a subject is more than 9 seconds is approximately 0.6915 or 69.15%.

*IG:whis.sama_ent*