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What is the standard deviation and what is the probability that a student scored higher than 322 if the mean test score is 312 and 16 percent of the scores are under 307?
Wiki User
∙ 6y ago
Assuming a normal distribution:
If 16% are less than 307, then 84% are greater than 307.
Using single tailed normal tables we want the z value which gives 84%-50% = 34% = 0.34 to the left of the mean; this is z ≈ -0.995
z = (value - mean)/standard deviation
→ standard deviation = (value - mean)/z ≈ (307 - 312)/-0.995 ≈ 5.03
The z value of 322 is z ≈ (322 - 312)/5.03 ≈ 1.99
Using the single tailed tables give the value of the normal distribution for z = 1.99 as approx 0.477 to the right of the mean.
This means that 0.477 + 0.5 = 0.977 are less than 322
→ 1 - 0.977 = 0.023 = 2.3 % are greater than 322
→ probability greater than 322 is 2.3%
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoThe SD is 5.03Pr(Test Score >= 322) = 2.3%
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