Question

Suppose that your statistics professor returned your first midterm exam with only a z-score written on it. She also told you that a histogram of the scores was mound shaped and approximately symmetric. How would you interpret each of the following z-scores?
a. 2.2
b. 0.4
c. 1.8
d. 1.0
e. 0

Answer 1

Answer:

A z-score specifies the number of standard deviations an observation is from the mean.  

Step-by-step explanation:

A z-score (aka, a standard score) specifies the number of standard deviations an observation is from the mean.  

The formula to compute the z-score is, $Z = \frac{X - \mu}{\sigma}$, where X = value of the random variable, µ = mean, σ = standard deviation.

The random variable X follows a Normal distribution with parameters µ and σ².

(a)

A z-score of 2.2 implies that the score in the first midterm exam is 2.2 standard deviations above the mean.

(b)

A z-score of 0.4 implies that the score in the first midterm exam is 0.4  standard deviations above the mean.

(c)

A z-score of 1.8 implies that the score in the first midterm exam is 1.8  standard deviations above the mean.

(d)

A z-score of 1.0 implies that the score in the first midterm exam is 1.0  standard deviations above the mean.

(e)

A z-score of 0 implies that the score in the first midterm exam is 0  standard deviations above the mean. That is the score in the first midterm exam is same as the mean score.