00:01
The producer of a weight loss pill made the claim that the weight loss after one week, we will call that random variable x, is normally distributed with the mean of 1 .75 pounds and a standard deviation of 0 .95 pounds.
00:17
And now we have a sample of 60 people, and in that sample, the mean weight lost after one week was 1 .73 pounds.
00:30
So we are asked if the producer's claim is correct, what is the probability that the mean weight loss of such a sample after one week on the pill would be 1 .73 pounds or less? so mathematically, that is, what is the probability that sample average is less than or equal to 1 .73? to answer this question, we must understand how the sample average would be to be to be to be distributed.
01:10
Since we are drawing our sample from a population that is normally distributed, therefore the sample averages are also normally distributed.
01:26
So that is, if we are just to continuously take samples of size 60 and calculate the average for the sample, the sample average would be normally distributed.
01:37
Furthermore, the standard deviation of sample averages is equal to the standard deviation of the population or of the individuals.
01:48
In the population divided by the square root of the sample size.
02:03
And this is equal to approximately 0 .126.
02:10
And regardless of the distribution of the population, the mean of sample averages would be equal to the mean of the population, and that is 1 .75.
02:25
So here we have completely defined the distribution of sample averages, which means we can calculate this probability...