00:01
For this exercise, we are told that the weights of skiers, it's called this random variable x, are normally distributed with the mean of 198 pounds and a standard deviation of 40 pounds.
00:14
And we have a gondola that can carry 25 skiers, and it's rated for a maximum load of 3 ,750 pounds.
00:23
So for the first question we are asked, what is the maximum mean weight of the passengers if the gondola is filled to its stated capacity of 25 passengers.
00:34
So the maximum total weight is 3 ,750.
00:40
If we divide that by the number of passengers, so give us the maximum average for the passengers, and this comes out to 150 pounds.
00:53
And so we are asked, what is the probability that their mean weight exceeds 150 pounds? so this is the probability that the sample mean is, greater than 150.
01:10
So you answer this, we have to know how sample means are distributed.
01:14
So that is if we continuously take samples of 25 skiers, the sample means would vary from sample to sample because the samples are random.
01:24
And so the sample mean has some distribution.
01:28
Now since the skier weights are normally distributed and the samples of 25 are drawn from the population of skiers, this means that sample means are also normally distributed.
01:46
And the mean of sample means is equal to the mean of the skier population, which is 198 pounds.
01:58
And the standard deviation of sample means is equal to the standard deviation of the population divided by the square root of the sample size...