Question

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.

Answer 1

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

Observation-

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.