Exam scores were normal in MIS 200. Jason's exam score was 1.41 standard deviations above the mean. what percentile is he in?
Exam scores were normal in MIS 200. Jason's exam score was 1.41 standard deviations above the mean. What percentile is he in?
To find the percentile of Jason's exam score, we need to use the Z-score formula. The Z-score measures how many standard deviations an observation is from the mean.
First, we need to find the Z-score. The formula is:
Z = (X - μ) / σ
Where:
Z is the Z-score,
X is the value we want to find the percentile of (Jason's exam score),
μ is the mean of the data (average score),
σ is the standard deviation of the data.
You mentioned that Jason's exam score was 1.41 standard deviations above the mean. This means that his Z-score is 1.41.
Now, we need to find the percentile associated with this Z-score. We can use a Z-score table or a calculator. Assuming a normal distribution, we can use a Z-score table.
By looking up the Z-score of 1.41 in the table, we find that it corresponds to a percentile of approximately 92.69%.
Therefore, Jason is in the 92.69th percentile.
To find out Jason's percentile based on his exam score, we need to use the concept of the standard normal distribution. Here are the steps to calculate it:
1. Find the Z-score: A Z-score represents the number of standard deviations an observation is from the mean. To find Jason's Z-score, we need the mean and standard deviation of the exam scores in MIS 200. Let's assume the mean is μ and the standard deviation is σ.
2. Calculate Jason's Z-score: Given that Jason's exam score is 1.41 standard deviations above the mean, we can use the formula:
Z = (x - μ) / σ,
where x is Jason's exam score.
3. Convert Z-score to percentile: Once we have Jason's Z-score, we can look up in a standard normal distribution table to find the corresponding percentile. The table provides the proportion of data below a particular Z-score. We are interested in finding the percentage of students with lower scores than Jason.
4. Interpret the percentile: The resulting percentile represents the proportion of scores that fall below Jason's score. For example, if the percentile is 80%, it means that Jason scored higher than 80% of the students in MIS 200.
Please note that to provide a precise calculation, we would need the mean and standard deviation of the exam scores in MIS 200.
Look up Z = 1.41 in the back of a statistics text in a table called something like "areas under a normal distribution." Since this is a percentile above the mean, the proportion is given in the larger part. Convert that to a percentile.
I hope this helps. Thanks for asking.