Question

4. The grades on a geometry midterm at Springer are roughly symmetric with μ=68 and σ=5.5. Emily scored 66 on the exam.

Answer 1

Answer:

$Z = 0.36$

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

In this problem:

I suppose there was a miscue in typing the names, either Emily is Jessica, or we have to find the z-score for Emily's exam.

We have that $\mu = 68, \sigma = 5.5$ and a score of 66, so $X = 66$

Then

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{66 - 68}{5.5}$

$Z = 0.36$