help on algebra 2

Question

Professor Herring is grading the final exam. He notices that the mean test score is 72, and the standard deviation is 6. The test scores were normally distributed.

If there were 300 students in the data sample, how many would have a test score between 72 and 78?*

how many students??

Answer 1

You'll need to find the z score for 72 and 78 and calculate the difference in the resulting probabilities.

z = (x - μ)/σ z₇₂ = (72 - 72)/6 =0, so there's a 50% probability of a student getting less than 72.

z₇₈ = (78 - 72)/6 = 1, so the probability of less than a 78 is 0.8413 or 84.13%.

THe difference between 50% and 84.13% is the probability of a student scoring between 72 and 78. Apply that figure to the 300 students to find the no. of students likely to have scores in that range.