Assume a set of test scores is normally distributed with a mean of 100 and a sta

Question

Assume a set of test scores is normally distributed with a mean of 100 and a standard deviation of 12.

A. what is the percentage of scores less then 88? ( I think it's 16%????)

B. what is the percentage of scores between 76 and 112? ( I think it's 81.5%????)

C. If you scored 115 on the test what is your z-score? (I think it's 1.25?????)

D. What percentage of people scored better then you if you scored 115? (I think it's 11%???)

I have answers for each problem please explain if I have them wrong.. Thanks :)

Explanation / Answer

yes your all ans are right reason take help The 68-95-99.7 rule states that in a normally distributed set of data, approximately 68% of all observations lie within one standard deviation either side of the mean, 95% lie within two standard deviations and 99.7% lie within three standard deviations. we get Or looking at it cumulatively: then 0.15% of the data lie below the mean minus three standard deviations 2.5% of the data lie below the mean minus two standard deviations 16% of the data lie below the mean minus one standard deviation 50 % of the data lie below the mean 84 % of the data lie below the mean plus one standard deviation 97.5% of the data lie below the mean plus two standard deviations 99.85% of the data lie below the mean plus three standard deviations so A normally distributed set of data with mean 100 and standard deviation of 20 means that a score of 140 lies two standard deviations above the mean. Hence approximately 97.5% of all observations are less than 140.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.