After taking an aptitude test, the computer told Bob that he had a z-score of 1.08. If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score? Select one or more:A-Bob did worse than the mean score. B-About 14% of students taking the aptitude test did better than Bob. C-Bob scored within 1 standard deviation of the mean score. D-About 14% of students taking the aptitude test did worse than Bob. E-Bob scored within 2 standard deviations of the mean score. F-Bob did better than the mean score.

Question

Lucille Blanchard

Mathematics

29 January, 06:23

After taking an aptitude test, the computer told Bob that he had a z-score of 1.08. If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score? Select one or more:A-Bob did worse than the mean score. B-About 14% of students taking the aptitude test did better than Bob. C-Bob scored within 1 standard deviation of the mean score. D-About 14% of students taking the aptitude test did worse than Bob. E-Bob scored within 2 standard deviations of the mean score. F-Bob did better than the mean score.

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Darion Dalton · Answer 1

B-About 14% of students taking the aptitude test did better than Bob.

E-Bob scored within 2 standard deviations of the mean score.

F-Bob did better than the mean score.

Step-by-step explanation:

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.

Bob had a z-score of 1.08. This means that in the test, his grade was 1.08 standard deviations above the mean.

A-Bob did worse than the mean score.

He has a positive z-score, which means that he did better than the mean score. So this option is not correct.

B-About 14% of students taking the aptitude test did better than Bob.

A z-score of 1.08 has a pvalue of 0.8599. So 85.99% of the students taking the test did worse than Bob and 100-85.99 = 14.01% did better than Bob. So this option is correct.

C-Bob scored within 1 standard deviation of the mean score.

His grade was 1.08 standard deviations above the mean, so more than one standard deviation of the mean score. So this option is not correct.

D-About 14% of students taking the aptitude test did worse than Bob.

A z-score of 1.08 has a pvalue of 0.8599. So 85.99% of the students taking the test did worse than Bob and 100-85.99 = 14.01% did better than Bob. So this option is not correct.

E-Bob scored within 2 standard deviations of the mean score.

His grade was 1.08 standard deviations above the mean, so within 2 standard deviations of the mean score. So this option is correct.

F-Bob did better than the mean score.

He has a positive z-score, which means that he did better than the mean score. So this option is correct.