Question

1. A math assignment has a µ = 41 and σ= 1.1. The teacher wants to know what raw scores represent the middle 72%. What are those values?

Answer 1

Given that,

mean = = 41

standard deviation = =

middle % of score is

P(-z < Z < z) = 0.72

P(Z < z) - P(Z < -z) =0.72

2 P(Z < z) - 1 =0.72

2 P(Z < z) = 1 + 0.72= 1.72

P(Z < z) = 1.72/ 2 = 0.86

P(Z <1.08 ) = 0.86

z  ± 1.08 using z table

Using z-score formula  

x= z * +

x= 1.08 *1.1+41

x= 42.188

x= z * +

x= -1.08 *1.1+41

x= 39.812

valures are

42.188 , 39.812