The grades on the last history exam had a mean of 80%. Assume the population of grades on history exams is known to be distributed normally, with a standard deviation of 5%. Using the empirical rule, approximately what percent of students earned a score between 70% and 80%? 3.5% 5% 47.5% 95%

Percent of students earned a score between 70% and 80% is 47.7% .

Step-by-step explanation:

We are given that the grades on the last history exam had a mean of 80%. Assume the population of grades on history exams is known to be distributed normally, with a standard deviation of 5%.

Let X = grades on history exams

So, X ~ N()

The standard normal z score distribution is given by;

          Z = ~ N(0,1)

So, percent of students earning a score between 70% and 80% is given by = P(0.70 < X < 0.80) = P(X  < 0.80) - P(X <= 0.70)

P(X < 0.80) = P( < ) = P(Z < 0) = 0.50 {using z table}

P(X <= 0.70) = P( <= ) = P(Z <= -2) = 1 - P(Z < 2) = 1 - 0.97725

                                                                                                 = 0.02275

So,  P(0.70 < X < 0.80) =  0.50 - 0.02275 = 0.47725 or 47.7%                                                        

Therefore, 47.7% of students earned a score between 70% and 80%.

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