Question

The grades on the last math exam had a mean of 88%. Assume the population of grades on math exams is known to be normally distributed with a standard deviation of 6. What percent of students earn a score between 72% and 90%?

0.6255

0.5843

0.6754

0.5346

Answer 1

@mathslover

Answer 2

@mtbender74

Answer 3

Let \(X\) be the grade of math exams. Since \(X\) is normally distributed, you can standardize it to find the probability asked. The question is asking \(P(72<X<90)\). Let's standardize:
\[ P(72<X<90)=P\left( \frac{72-88}{6}<\frac{X-88}{6}<\frac{90-88}{6}\right)=P(-2.67<Z<0.33)\]

You will then need to find the area under the standard normal distribution between -2.67 and 0.33

Answer 4

http://en.wikipedia.org/wiki/Standard_normal_table#Cumulative_from_mean_.280_to_Z.29