Question

A fitness company surveyed the weights of its 90 costumers. Assume that the weights are normally distrubted with a mean of 162 lbs and a standard deviation of 3.5 lbs. If you select one of its costumers randomly, what is the probability that the costumer's weight is
a) more than 162 lbs?
b) more than 155 lbs?
c) less than 172.5 lbs?
d) between 158.5 lbs and 169 lbs?

Answer 1

a) 50%
b) 97.7%
c) 99.9%
d) 81.9%

These answers were obtained using the normal disribution calculation tool at
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html

I did not make use of the fact that the mean and standard deviation were obtained from 90 samples. I assumed 162 was the true mean and 3.5 was the true std deviation.