Question

In a given year, the grade point average (GPA) of Statistics majors at the University of South Carolina is Normally distributed with and . Answer the following. ?=2.1?=0.25a. What GPA interval contains the middle 95% of all students? Sketch this.

Answer 1

Solution:-

Given that,

mean = = 2.1

standard deviation = = 0.25

middle 95%

P(-z Z z) = 0.95

P(Z z) - P(Z -z) = 0.95

2P(Z z) - 1 = 0.95

2P(Z z) = 1 + 0.95 = 1.95

P(Z z) = 1.95 / 2 = 0.975

P(Z 1.96) = 0.975

z = - 1.96, +1.96

Using z-score formula,

x = z * + = -1.96*0.25+2.1= 1.61

x = z * + = 1.96*0.25+2.1 = 2.59

Answer = two valuues = 161 and 2.59