Respuesta :
Answer:
Due to the higher z-score, David has the higher standardized score
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.
Which student has the higher standardized score
Whoever had the higher z-score.
David:
Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. So [tex]X = 52, \mu = 70, \sigma = 11[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 70}{11}[/tex]
[tex]Z = -1.64[/tex]
Steven:
Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. So [tex]X = 52, \mu = 64, \sigma = 6[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 64}{6}[/tex]
[tex]Z = -2[/tex]
Due to the higher z-score, David has the higher standardized score
