A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. if 67.36% of his students received grades of c or above, what is the minimum score of those students receiving a grade of at least a c?

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Mathematics

Mills

15 September, 23:40

A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. if 67.36% of his students received grades of c or above, what is the minimum score of those students receiving a grade of at least a c?

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Jovany Weber · Answer 1

72.45 Since 67.36% is greater than 50%, we know that the cutoff will be at a negative value. And we need to lookup in a standard normal table for the value of 67.36 - 50 = 17.36. That value will happen with a z value of 0.45. Now multiply the standard deviation of 9 by 0.45 to get 4.05. That means that the cutoff value for the student getting a C or above is the mean minus 4.05, so 76.5 - 4.05 = 72.45