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?

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?
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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 whichgives 84%-50% = 34% = 0.34 to the left of the mean; this is z ≈-0.995z = (value - mean)/standard deviation→ standard deviation = (value - mean)/z ≈ (307 - 312)/-0.995 ≈5.03The z value of 322 is z ≈ (322 - 312)/5.03 ≈ 1.99Using the single tailed tables give the value of the normaldistribution for z = 1.99 as approx 0.477 to the right of themean.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%
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