Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
First, let's calculate the SEM:
SEM = SD / √n
Given that the standard deviation (SD) is 7.73 and the sample size (n) is 24, we can compute the SEM as follows:
SEM = 7.73 / √24 ≈ 1.57
Next, we need to standardize the value of 69 by using the formula for z-score:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, we want to standardize 69 with a mean of 73 and a standard deviation of 7.73:
z = (69 - 73) / 7.73 ≈ -0.52
Now that we have the z-score, we can find the corresponding area under the normal distribution curve using a standard normal table or a statistical calculator. The area to the left of the z-score represents the percentage of sample means that are less than 69.
Using a standard normal table or calculator, we find that the area to the left of -0.52 is approximately 0.3015. This means that approximately 30.15% of sample means are less than 69.
So, the answer is that approximately 30.15% of sample means are less than 69.