Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1548 and the standard deviation was 319. The test scores of four students selected at random are 1990​, 1280​, 2240​, and 1450. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

Answer 1

Step-by-step explanation:

z-score is:

z = (x − μ) / σ

For the four students:

z = (1990 − 1548) / 319 = 1.39

z = (1280 − 1548) / 319 = -0.84

z = (2240 − 1548) / 319 = 2.17

z = (1450 − 1548) / 319 = -0.31

z-scores are considered significant if they are less than -2 or greater than 2.  So the third student's score is unusual.

Answer 2

The Zscore value is the number of standard deviations a given score is from the mean of the distribution. The Zscore values are ; 1.386, - 0.840, 2.169 and -0.307 respectively.

None of the values are unusual.

Given the Parameters :

• Mean, μ = 1548
• Standard deviation, σ = 319

The test scores, X ; 1990, 1280, 2240, 1450

Recall :

• Zscore = (X - μ) ÷ σ

For X = 1990 ;

Zscore = (1990 - 1548) / 319 = 1.386

For X = 1280 ;

Zscore = (1280 - 1548) / 319 = - 0.840

For X = 2240 ;

Zscore = (2240 - 1548) / 319 = 2.169

For X = 1450 ;

Zscore = (1450 - 1548) / 319 = - 0.307

Therefore, the corresponding Zscore values for 1990, 1280, 2240 and 1450 are 1.386, -0.840, 2.169 and -0.307 respectively

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