## 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

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## Answers ( )

Answer:[tex]Z = 0.36[/tex]

Step-by-step explanation:Z-score:In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X – \mu}{\sigma}[/tex]

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 [tex]\mu = 68, \sigma = 5.5[/tex] and a score of 66, so [tex]X = 66[/tex]

Then

[tex]Z = \frac{X – \mu}{\sigma}[/tex]

[tex]Z = \frac{66 – 68}{5.5}[/tex]

[tex]Z = 0.36[/tex]

Answer:0.50

Step-by-step explanation:just did it on khan