The scatter plot shows the relationship between the test scores of a group of students and the number of hours they spend on soc
ial media in a week:
Part A: What is the group of points labeled A called? What is the point labeled B called? Give a possible reason for the presence of point B. (3 points)
Part B: Describe the association between a student’s test scores and the number of hours spent on social media. (2 points)
Part A: What is the group of points labeled A called? What is the point labeled B called? Give a possible reason for the presence of point B. (3 points)
Part B: Describe the association between a student’s test scores and the number of hours spent on social media. (2 points)
1 answer:
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Answer:
a) 6.68th percentile
b) 617.5 points
Step-by-step explanation:
Problems of normally distributed samples are 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:
a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.
has a pvalue of 0.0668
So this student is in the 6.68th percentile.
b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.
He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.