The Central Limit Theorem
Not always practical or possible to investigate an entire population, so we must investigate samples. How will the means of samples differ from the mean of the population?
Distribution of Sample Means:
Properties of Distribution of Sample Means:
When ALL possible samples of a specific size are selected with replacement from a population, then:
AS SAMPLE SIZE N INCREASES WITHOUT LIMIT, THE SHAPE OF THE DISTRIBUTION OF THE SAMPLE APPROACHES A NORMAL LIMIT.
When sample means are involved, must use: or where = sample mean.
The average number of pounds of sugar that a person living in Sugarland consumes each year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal.
a) Find the probability that a person selected at random consumes less than 224 pounds per year.
b) If a sample of 40 individuals is selected, find the probability that the mean of the sample will be less than 224 pounds per year.