Sampling Distribution of a Linear Combination of Means (4 of 4)
Next section: Pearson's correlation
The sampling distribution of L therefore has a mean of 16 and a standard
deviation of 4.33. The question is, what is the probability of getting
a value of L greater than or equal to 15? The formula:
=
(15 - 16)/4.33 = -0.23
can be used to find out how many standard deviations above μ
L
an L of 15 is.
Using a
z table,
it can be determined that 0.41 of the time a z of -0.23 or lower would
occur. Therefore the probability of a z of -0.23 or higher occurring is (1
- 0.41) = 0.59. So, the probability that
is
greater than 15 is 0.59.
Next section: Pearson's correlation