Question

The amount of time that a drive-through bank teller spends on a customer is a random variable with a mean   3.1 minutes and variance 2.65 . If a random sample of 51 customers is observed. (a) Find the probability that their mean time at the teller’s window is at least 3.2 minutes but less than 3.4 minutes (a) Find the probability that their variance at the teller’s window is not more than 1.7855.

Answer 1

a)

µ =    3.1                                  
σ =    1.62788206                                  
n=   51                                  
                                      
P(   3.2   ≤ X ≤    3.4   )                      
Z1 = (X1 - µ )/(σ/√n) =   (3.2-3.1)/(1.62788205960997/√51)=               0.44                  
Z2 = (X2 - µ )/(σ/√n) =   (3.4-3.1)/(1.62788205960997/√51)=               1.32                  
P (   3.2   < X <    3.4   ) =    P (    0.44   < Z <    1.32   )   
= P ( Z <    1.316   ) - P ( Z <   0.439   ) =    0.9059   -    0.6696   =    0.2364   (answer)

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