Which of the three runners have the fastest pace? Explain how you know.
1 answer:
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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 and standard deviation
, the zscore of a measure X is given by:
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 .
You scored 24 on Exam A. So
The composite score on Exam B is approximately normally distributed with mean 1031 and standard deviation 215.
This means that .
You scored 1167 on Exam B, s:
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.