Question

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 11.2 minutes and a standard deviation of 2.1 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 7 and 13 minutes

(b) the response time is less than 7 minutes

(c) the response time is more than 13 minutes

Answer 1

a)

µ =    11.2                              
σ =    2.100                              
we need to calculate probability for ,                                  
7   ≤ X ≤    13                          
X1 =    7   ,   X2 =   13                  
                                  
Z1 =   (X1 - µ ) / σ = (   7   -   11.2   ) /    2.1   =   -2.0000  
Z2 =   (X2 - µ ) / σ = (   13   -   11.2   ) /    2.1   =   0.8571  
                                  
P (   7   < X <    13   ) =    P (    -2   < Z <    0.857   )
                                  
= P ( Z <    0.857   ) - P ( Z <   -2.000   ) =    0.80432   -    0.022750   =    0.7816

b)

µ =    11.2              
σ =    2.1              
left tailed                  
P( X ≤    7   )          
                  
Z =(X - µ ) / σ = (   7   -   11.2   ) /    2.1
Z =    -2.000              
P(X ≤   7   ) = P(Z ≤   -2.00   ) =   0.0228(answer)
excel formula for probability from z score is =NORMSDIST(Z)                  

c)

µ =    11.2                          
σ =    2.1                          
right tailed                              
P ( X ≥   13.00   )                      
                              
Z =   (X - µ ) / σ = (   13.00   -   11.2   ) /    2.1   =   0.857
                              
P(X ≥   13   ) = P(Z ≥   0.857   ) =   P ( Z <   -0.857   ) =    0.1957(answer)
excel formula for probability from z score is =NORMSDIST(Z)