search for: 40km

This is probably embarrassingly basic, but I have spent quite a few hours in Google and RSeek without getting a clue - probably I'm asking the wrong questions... There is this guy who has decided to walk through Australia, a total distance of 4000 km. His daily portion (mean) is 40km with an sd of 10 km. I want to calculate the number of days it takes to arrive with 80, 90, 95, 99% probability. I know how to do this manually, eg. for 95% $\Phi \left( \frac{4000-40n}{10 \sqrt{n}} \right) \leq 0.05$ find the z score... but how would I do this in R? Not qnorm(), but what is it?...

...j=longlat +datum=WGS84")) and then reprojecting it to Berhmann with: spPointReprj=spTransform(Data,CRS("+proj=cea +lon_0=0 +lat_ts=30 +x_0=0 +y_0=0 +ellps=WGS84")) If I put the two outputs of the reprojections in the same map, they are off by few meters in the tropics by up to 40km in the poles. I decided to investigate how the reprojections are done and my calculations are different from both R and ArcGis: First, I calculated the radious of the Earth in two different ways: =Re * (1 - e^2)/ (1 - e^2 *SIN(RADIANS(Latitude))^2)^(3/2) =Re * SQRT(1 - e^2) / (1 - e^2 * (SIN(RA...