Answer:
a) A z-score of 2.49 means that your grade was 2.49 standard deviations above the mean of all grades.
b) 1.39% of the class scored lower than your friend.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
You got a score of 2.49 on an exam.
(a) Write a sentence explaining what that means
A z-score of 2.49 means that your grade was 2.49 standard deviations above the mean of all grades.
(b) Your friend got a z-score of negative 2−2. If the grades satisfy the Nearly Normal Condition, about what percent of the class scored lower than your friend?
This percentage is the pvalue of
So 0.0139 = 1.39% of the class scored lower than your friend.