Respuesta :
Answer:
B.The score on Exam A is better, because the percentile for the Exam A score is higher.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
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.
In this problem, we have that:
Two exams. The exam that you did score better is the one in which you had a higher zscore.
The composite score on Exam A is approximately normally distributed with mean 20.1 and standard deviation 5.1.
This means that [tex]\mu = 20.1, \sigma = 5.1[/tex].
You scored 24 on Exam A. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 20.1}{5.1}[/tex]
[tex]Z = 0.76[/tex]
The composite score on Exam B is approximately normally distributed with mean 1031 and standard deviation 215.
This means that [tex]\mu = 1031, \sigma = 215[/tex].
You scored 1167 on Exam B, s:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1167 - 1031}{215}[/tex]
[tex]Z = 0.632[/tex]
You had a better Z-score on exam A, so you did better on that exam.
The correct answer is:
B.The score on Exam A is better, because the percentile for the Exam A score is higher.
