Answer:
The maximum time guaranteed = 19.04 minutes. 
Explanation:
From the given problem data, we have: 
Let Y be the random variable which follows the normal distribution. 
So, 
Y ~ N(u = 15, SD = 2.4
Where, u = mean and SD = Standard Deviation
Let the maximum time guaranteed is = M
So, 
P (Y > M) = 0.05   equation 1
Convert this equation 1 into standard normal variable, that is, 
P(Y> M) = 0.05
1 -  P(Y  M) = 0.05
 M) = 0.05
P(Y  M) = 1 - 0.05
 M) = 1 - 0.05
P(Y  M) = 0.95
 M) = 0.95
P = 0.95
 = 0.95
P ( Z  )  = 0.95     Equation 2
 )  = 0.95     Equation 2
From the equation 2, we have, 
 = 1.644853627
 = 1.644853627   
1.644853627 value is from using the function of Excel
( =NORSINV(0.95)) = 1.644853627
So, 
M = 1.644853627 + 2.4 + 15
M = 19.04 
Hence, the maximum time guaranteed = 19.04 minutes.