00:01
We're given that a study of high -risk drivers was taken, and they determined that the probability the driver would have an accident within 50 days is about 30 % or 3 out of 10.
00:16
And we're given that this is modeled by an exponential distribution, and so we're asked if we take a random sample of 100 of these high -risk drivers, what's the probability that they have an accident within 80 days? so the issue is, again, we need to find the constant mu in the exponential distribution.
00:40
So from what we're given, we know this is the integral from 0 to 50 of 1 over mu, e to the minus x over mu.
00:49
That's the pdf.
00:53
Okay, and when we evaluate this integral, it will work out to be 1 minus e to the minus 50 over mu.
01:03
Okay, so now we can solve for mu.
01:09
I should get this as equal to 7 over 10.
01:11
And now if i take natural log of both sides and solve for mu, i should get that mu is equal to minus 50 over the natural log of 7 tenths...