This is correct

This is incorrect. You correctly computed the z-scores but did not convert those into probabilities correctly.

b)

x= length of time

μ = 15

σ= 4.75

P(13<x<16) For x=13, z= (13-15)/4.75 -> -0.421

For x=16, z= 16-15/4.75 -> 0.210

P(13<x16) = P(-0.412<z< 0.210)

0.416-0.340= 0.076