Assume that scores on the verbal portion of the GRE (Graduate Record Exam) follow the normal distribution with mean score 151 and standard deviation 7 points, while the quantitative portion of the exam has scores following the normal distribution with mean 153 and standard deviation 7.67. Use this information to answer the following a) Find the score of a student who scored in the 80th percentile on the Quantitative Reasoning section of the exam. (please round to two decimal places) b)Find the score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section of the exam please round to two decimal places)

a) 159.44

b) 147.33

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:

Verbal portion of GRE:

Quantitative portion of GRE:

a) Find the score of a student who scored in the 80th percentile on the Quantitative Reasoning section of the exam. (please round to two decimal places)

Value of X when Z has a pvalue of 0.8. So X when Z = 0.84.

b)Find the score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section of the exam please round to two decimal places)

Value of Z when Z has a pvalue of 1-0.7 = 0.3. So X when Z = -0.525. So

24 units

step-by-step explanation:

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step-by-step explanation: