00:01
Here we are told that the time that a customer spends waiting at a check -in counter at an airport is a random variable with mean of 8 .2 minutes and standard deviation of 1 .5 minutes.
00:13
Then a random sample of 49 customers is observed.
00:21
And we are asked to find some probabilities.
00:23
For part a, we are asked to find the probability that the waiting time is less than 10 minutes.
00:33
This is the average waiting time of the sample.
00:40
So we have not been told much about the shape of the distribution of the overall population of waiting times.
00:48
However, since our sample size is 49 and we're dealing with the sample average, we can say that the sample averages are approximately normally distributed.
01:01
And we can also say that the mean of sample averages is the population mean, which is 8 .2.
01:09
And the standard deviation of sample averages is equal to the population standard deviation over the square root of the sample size, which is equal to 1 .5 divided by 7 or 0 .23.
01:35
So sample averages are approximately normally distributed...