Question is bellow

Question

The scores on a math test are normally distributed with a mean of 78 and a standard deviation of 6. The test scores range from 0 to 100. Nineteen students had test scores between 72 and 90. Estimate the number of students who took the test.

About  students took the test.

Answer 1

Based on the normal curve probabilities:

there is 34.1% between the mean (78) and minus one standard deviations (72). There is another 34.1% between the mean (78) and plus one standard deviation (84) and there is 13.6% between plus one standard deviations (84) and plus 2 standard deviations (90). These total to 81.8%.

So, letting "N" be the number of students, we can say that 0.818N = 19 or N = 23,227 or 23 students