00:01
Some population has a normal distribution with a mean of 45 .3 and a standard deviation of 48 .4.
00:08
We're going to draw from this population a random sample of size 23.
00:20
But for the first question, we were asked for the probability that a single randomly selected value from this population is less than 29 .2.
00:29
So what is the probability that x is smaller than 29 .2? one way to solve this is to use software such as excel.
00:40
In excel we want to find the normal distribution function.
00:44
We enter 29 .2 for the first argument, then we enter the mean and standard deviation of the distribution, and then for the cumulative argument we enter true to get the probability of a value anywhere up to 29 .2.
01:01
We hit enter and we get 0 .4860 approximately.
01:09
And the second question is what is the probability that the sample mean for the sample of size 23 will be less than 29 .2.
01:19
So the sample has some sample mean which vary from random sample to random sample.
01:25
We want the probability that this mean is less than 29 .2.
01:34
So we need to know the sampling distribution of sample means.
01:39
Because the population is normally distributed this means that for a given sample size the sampling distribution sample means drawn from this population are also normal.
01:49
The mean of the sampling distribution of sample means is equal to the population mean, and the standard deviation of the sampling distribution of sample means is the population standard deviation over the square root of the sample size...