Question

The mean test score in her upcoming class is 49, and the standard deviation is 20.7. The teacher wants to identify those students who may need extra challenges. As a first cut, she decides to look at students who have z-scores above z = 2.00 Identify the test score corresponding to a z-score of above z=2.00. Round to the nearest whole number.

Answer 1

Answer:

Students who have z-scores above z = 2.00 are the ones who scored above 90.4.

Step-by-step explanation:

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

$Z = \frac{X - \mu}{\sigma}$

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.

The mean test score in her upcoming class is 49, and the standard deviation is 20.7.

This means that $\mu = 49, \sigma = 20.7$

Identify the test score corresponding to a z-score of above z=2.00.

As X increases, so does the z-score. So those scores are higher than X when Z = 2.

$Z = \frac{X - \mu}{\sigma}$

$2 = \frac{X - 49}{20.7}$

$X - 49 = 2*20.7$

$X = 90.4$

Students who have z-scores above z = 2.00 are the ones who scored above 90.4.