Suppose your statistics professor reports test grades as z-scores, and you got a score of 2.49 on an exam. (a) Write a sentence explaining what that means. (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?

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.

the answers c