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Given μ=110 and σ=10 in a college entrance examination, find the corresponding z-value of the scores gained by the following students. Show all the solutions and sketch it graph.

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Answer:

Question

Given μ=110 and σ=10 in a college entrance examination, find the corresponding z-value of the scores gained by the following students. Show all the solutions and sketch it graph.

1. X=98

2. X=65

3. X=120

4. X=74

5. X=135

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Expert Answer

Step 1

Given Information:

Mean μ=110μ=110

Standard deviation σ=10σ=10

Z-score is a measure which indicates how many standard deviations away, a data value is, from the mean. It is given by the formula:

z=X−μσz=X-μσ

1) Z-score for X = 98:

z=98−11010=−1.2z=98-11010=-1.2

This, means that X = 98 is 1.2 standard deviations below the mean.

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