Mathematics
mkinsel40
19

The average score on a standardized test is 500 points with a standard deviation of 50 points. If 2,000 students take the test at a local school, how many students do you expect to score between 500 and 600 points?

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(1) Answers
Mireille708

To solve this problem, we use the z statistic. The formula for z score is given as: z = (x – u) / s Where, x = sample score u = the average score = 500 s = standard deviation = 50   First, we calculate for z when x = 500 z = (500 – 500) / 50 z = 0 / 50 z = 0 Using the standard z table, at z = 0, the value of P is: (P = proportion) P (z = 0)= 0.5   Secondly, we calculate for z when x = 600 z = (600 – 500) / 50 z = 100 / 50 z = 2 Using the standard z table, at z = 2, the value of P is: (P = proportion) P (z = 2) = 0.9772   Since we want to find the proportion between 500 and 600, therefore we subtract the two: P (500 ≥ x ≥ 600) = 0.9772 – 0.5 P (500 ≥ x ≥ 600) = 0.4772   Answer: Around 47.72% of students have score from 500 to 600.

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