A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1461 and the standard deviation was 318. The test scores of four students selected at random are 1900, 1180, 2160, and 1360
Find the z-scores that correspond to each value and determine whether any of the values are unusual.
Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice.
Suppose, random variable X denotes the exam's scores.
The sample values are as follows.
Standard normal variate Z is defined as Z=(X-1461)/318
So, corresponding z-scores are given by
In general, we consider 3 standard deviation interval as this interval contains 99.73% values while 2 standard deviation interval contains 95.45% values.
We observe that, all the values are lying in the 3 standard deviation interval which is clear as z-scores are in the interval (-3,3).
So, we can conclude that there is no unusual value in the given sample observations.
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