Question

.Find the Z-sCore corresponding to the given value and use the z-SCore to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A test score of 50.0 on a test having a mean of 69 and a standard deviation of 10.

a. 1.9; not unusual

b. -19; unusual

c. -1.9; unusual

d. -1.9; not unusual

Answer 1

d. -1.9; not unusual

Explanation:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that;

`X = 50, \mu = 69, \sigma = 10`.

So

`Z = (X - \mu)/(\sigma)`

`Z = (50 - 69)/(10)`

`Z = -1.9`

A z-score of -1.9 is higher than -2 and lower than 2, so it is not unusual.

So the correct answer is:

d. -1.9; not unusual