14 Over 350 students took a college calculus final exam The

14. Over 350 students took a college calculus final exam. The scores of the students ratio\'s a normal distribution. Using the information given below. determine the mean and the standard deviation for the students\' scores. Give your answers to the nearest tenth of a percent. 32% of the students scored either less than 633% or more than 859%. Only the top 2.5% of students scored higher than a 91% on the exam.

Solution

As 32% of the students scored either less than 63.3% or more than 85.9%, then by symmetry, the mean is the middle of this interval,

u = (63.3 + 85.9)/2 = 74.6

As the right tailed area of 97% is 0.025, then the corresponding z score to it is, by table/technology,

z = 1.959963985

Thus, as

sigma = (x-u)/z

Then

sigma = (97 - 74.6)/1.959963985 = 11.42878143

Thus,

u = mean = 74.6
sigma = standard deviation = 11.42878143 [ANSWERS]