Consider the following.
(a) What percentage of a normal distribution is greater than the mean? (Give your answer correct to the nearest percent.)
Incorrect: Your answer is incorrect. . %
(b) What percentage is within 1 standard deviation of the mean? (Give your answer correct to the nearest percent.)
Correct: Your answer is correct. . %
(c) What percentage is greater than a value that is 1 standard deviation below the mean? (Give your answer correct to the nearest percent.)
Incorrect: Your answer is incorrect. . %
you can play around with Z-table numbers at
http://davidmlane.com/hyperstat/z_table.html
To answer these questions correctly, we need to understand the properties of a normal distribution and how to use z-scores to calculate percentages.
(a) What percentage of a normal distribution is greater than the mean?
In a normal distribution, 50% of the values are greater than the mean, and 50% are lower. This means that 50% of the distribution is greater than the mean. Therefore, the correct answer is 50%.
(b) What percentage is within 1 standard deviation of the mean?
In a standard normal distribution, approximately 68% of the values fall within 1 standard deviation of the mean. Since the standard normal distribution is symmetric, this means that approximately 34% of the values are both greater than the mean and within 1 standard deviation of the mean, and approximately 34% are both lower than the mean and within 1 standard deviation of the mean. Therefore, the correct answer is 34%.
(c) What percentage is greater than a value that is 1 standard deviation below the mean?
When we move 1 standard deviation below the mean in a standard normal distribution, we get a z-score of -1. A z-score represents the number of standard deviations an observation is from the mean. In a standard normal distribution, we can look up the percentage greater than a given z-score in a z-table. Looking up -1 in the z-table, we find that approximately 84.13% of the values are greater than a value that is 1 standard deviation below the mean. Therefore, the correct answer is approximately 84%.