Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar (s). The grades received by 200 students follow a normal distribution. The mean of the grades is 70%, and the standard deviation is 7%. The number of students who received a grade greater than 70% is about , and the number of students who got a grade higher than 84% is about .

Question

Mathematics

Snuggles

25 July, 12:54

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar (s). The grades received by 200 students follow a normal distribution. The mean of the grades is 70%, and the standard deviation is 7%. The number of students who received a grade greater than 70% is about , and the number of students who got a grade higher than 84% is about .

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Kirby · Answer 1

100 5

Step-by-step explanation:

a) The mean of a normal distribution is also the median. Half the population will have values above the mean. Half of 200 is 100, so ...

... 100 students will have grades above 70%.

b) 84% is 14% above the mean. Each 7% is 1 standard deviation, so 14% is 2 standard deviations above the mean. The empirical rule tells you 95% of the population is within 2 standard deviations of the mean, so about 5% of students (10 students) got grades higher than 84% or lower than 56%. The normal distribution is symmetrical, so we expect about 5 students in each range.

... about 5 students will have grades above 84%.