Question

)A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons.

What proportion of all tanks will hold between 14.75 and 15.10 gallons of gas?

Answer 1

find z values
\[z = \frac{x - mean}{stdev}\]
look up values in table to get probabilities
P(a<Z<b) = P(Z<b) - P(Z<a)

http://en.wikipedia.org/wiki/Standard_normal_table#Cumulative_table

also if z is negative, look up pos z then subtract from 1
P(Z<-a) = 1 - P(Z<a)