A manufacturer of bike racks for cars claims that the assemb

A manufacturer of bike racks for cars claims that the assembly time X for a particular model is normally distributed with a mean of 1 hour and a standard deviation of 0.10 hours. Find the probability that it takes between 0.8 hours and 1.1 hours to assemble a bike rack of this model.

Solution

So the probability is

P(0.8<X<1.1) = P((0.8-1)/0.1 <(X-mean)/s <(1.1-1)/0.1)

=P(-2<Z<1) = 0.8186 (from standard normal table)