SOLUTION: A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 15. Overall 5 students failed the te

Question 507442: A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 15. Overall 5 students failed the test, how many students were enrolled in her course?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 15. Overall 5 students failed the test, how many students were enrolled in her course?
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Assuming the failure cutoff is 70%,
z(70) = (70-78)/15 = -0.5333
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P(z < -0.333) = normalcdf(-100,-0.5333) = 0.2959
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Let x be the number students enrolled in the course:
Solve: 0.2959x = 5 students
x = 5/0.2959
x = 16.84
Round up to 17 students in the class.
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Cheers,
Stan H.
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