p (μ - kσ <= x <= μ + kσ)= .754 solve for k

Question

I was given the following equation and asked to solve for k. I worked part of it out and also took the normsinv(.754)=0.6871. I have no idea if I am on the right track. I would appreciate any help.

Answer 1

z=(X-µ)/s where s=standard deviation and X is a data value. To estimate the range of values of x between the limits for which the probability is 0.754, that is, the area under the normal distribution curve is 0.754. We need a value for z where P(z)-P(-z)=0.754. P(-z)=1-P(z), so P(z)-(1-P(z))=0.754; 2P(z)-1=0.754 so P(z)=0.877. This corresponds to z=1.16. Therefore, 1.16=(X-µ)/s. 1.16s=X-µ. Therefore, k=1.16 so that µ-1.16s<x<µ+1.16s.