00:01
This problem says suppose college students average 7 .3 hours of sleep per night with a standard deviation of 45 minutes and suppose that it's normally distributed.
00:09
What's the probability that a randomly selected college student sleeps more than 8 .1 hours? and also, we want to find what's the 60th percentile for college student sleep times, rounding both of our answers to four decimal places.
00:20
So first, for our probability of more than 8 .1 hours, we can, since this is normally distributed, use normal cdf in our calculator.
00:29
And for normal cdf, we need four values.
00:33
And it starts off with our lower and upper bound.
00:36
And then it finishes with our mean or our average and our standard deviation.
00:42
And for us, the lower and upper bound will come from the probability we're focused on because if we want more than 8 .1 hours, that means we want everything to the right of 8 .1 in our curve.
00:51
So our lower bound would be 8 .1 and our upper bound will use infinity just to show that we want everything to the right of the curve.
00:59
So that will include everything.
01:00
And then for our mean, we're given 7 .3 hours.
01:04
But we need to be careful with our standard deviation because everything that we have as far as units is built off of hours...