a final exam in statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?
Here you are dealing with means rather than individual scores.
Z = (score-mean)/SEm
SEm = SD/√n
Use same table as indicated in your later post.
where is this formula located on excel?
To find the percentage of sample means that are less than 70, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
Given that the population mean (μ) is 73 and the standard deviation (σ) is 7.73, we can calculate the standard error of the mean (SE) using the formula:
SE = σ / √n,
where n is the sample size. In this case, n = 24.
SE = 7.73 / √24 ≈ 1.582
To determine the Z-score for a sample mean of 70, we can use the formula:
Z = (x - μ) / SE,
where x represents the sample mean. Plugging in the values:
Z = (70 - 73) / 1.582 ≈ -1.895
To find the percentage of sample means that are less than 70, we need to find the area to the left of the Z-score (-1.895) in the standard normal distribution table.
Using the Z-table or a statistical software, we can find that the area to the left of -1.895 is approximately 0.0287.
Therefore, the percentage of sample means that are less than 70 is approximately 0.0287 * 100 = 2.87%.