Question 1182608
X~N(129.95, 5.1984) units seconds, seconds^2 (use the variance)
z=(x-mean)/sd
z=-3.78/2.28=-1.658
z=(-2.04/2.28)=-0.895
that probability is 0.1367
can check with 2ndVARS2(normalcdf(126.17,127.91,129.95,2.28)ENTER which is unrounded and 0.1368. I would use the first, unless the course requires no rounding of the z-value until the end.

The fastest 4% of laps: z(0.04), since want the shortest time, z=-1.7506
-1.7506=(x-129.95)/2.28
=125.96 seconds
-
This requires z (0.3) and z(0.7), which are -0.5244 and +0.5244 respectively
-0.5244=(x-129.95)/2.28
x=128.75 sec
and
x=131.15 sec
If this is checked, it is about 0.4013 of the laps, the discrepancy's being that the multiplying z by -0.5244 gives 1.1956 seconds, which was rounded upward to 1.20 seconds.