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