## 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. Find the z-scor

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.
Find the z-score for Jessica’s exam grade. Round to two decimal places.

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5 months 2021-12-29T07:56:11+00:00 2 Answers 0 views 0

$$Z = 0.36$$

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

$$Z = \frac{X – \mu}{\sigma}$$

$$Z = \frac{66 – 68}{5.5}$$

$$Z = 0.36$$