Question

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1468 and the standard deviation was 314. The test scores of four students selected at random are 1890, 1220, 2180, and 1360.

Find the z-scores that correspond to each value and determine whether any of the values are unusual.

The z-score for 1890 is __.

The z-score for 1220 is __.

The z-score for 2180 is __.

The z-score for 1360 is __.

Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. The unusual value(s) is/are __. (Use a comma to separate answers as needed.)

B. None of the values are unusual.

Answer #1

Here, μ = 1468, σ = 314 and x = 1890. We need to compute P(X <= 1890). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ

z = (1890 - 1468)/314 = 1.34

The z-score for 1890 is 1.34

Here, μ = 1468, σ = 314 and x = 1220. We need to compute P(X <=
1220). The corresponding z-value is calculated using Central Limit
Theorem

z = (x - μ)/σ

z = (1220 - 1468)/314 = -0.79

The z-score for 1220 is -0.79

Here, μ = 1468, σ = 314 and x = 2180. We need to compute P(X <=
2180). The corresponding z-value is calculated using Central Limit
Theorem

z = (x - μ)/σ

z = (2180 - 1468)/314 = 2.27

The z-score for 2180 is 2.27

Here, μ = 1468, σ = 314 and x = 1360. We need to compute P(X <= 1360). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ

z = (1360 - 1468)/314 = -0.34

The z-score for 1360 is -0.34

B. None of the values are unusual

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