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Chi-squared link to gamma


Apr 11, 2016
I'm not quite sure how to solve the question with two approaches.

Let X be the time taken for the cars to arrive.

Given that 1 car passes every 2 mins, theta = 2.
We are interested in the 10th car that passes so alpha = 10.
Thus I know the distribution is Gamma~(theta=2,alpha=10)
I can solve this using the gamma distribution to find P(X>28.41). (Although the summation is from k= 0 to 9 which is pretty tedious)

To relate the chi-squared in this case, r = 20 while theta = 2, but I don't see how I can solve P(X>28.41) because it goes back to the gamma distribution.

How do I solve this using the chi-squared distribution?