Sampling Distribution of a Linear Combination of Means (4 of 4)


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 μL 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.