Mrs. Marble gave her 5th grade class a math test. The scores reflect a relatively normal distribution. The mean score for the group was 80 with a standard deviation of 8. Based upon this information, answer the following questions:
Bobby scored exactly two standard deviations above the mean. What was Bobby’s score on the test? __ ___
I bet he scored 80+2*8=96
z = (x-u)/S
2 = (x-80)/8
16 = (x-80)
x=96
To find Bobby's score on the test, we need to calculate how many standard deviations his score is above the mean, and then use that information to determine his actual score.
Given that the mean score for the class was 80 and the standard deviation was 8, we can calculate the number of standard deviations Bobby's score is above the mean by using the formula:
Number of standard deviations = (Bobby's score - Mean score) / Standard deviation
Since Bobby's score is exactly two standard deviations above the mean, we can take the formula and rearrange it to solve for Bobby's score:
Bobby's score = (Number of standard deviations * Standard deviation) + Mean score
Substituting the values we know, we get:
Bobby's score = (2 * 8) + 80
Bobby's score = 16 + 80
Bobby's score = 96
Therefore, Bobby's score on the test was 96.