Question

Tire pressure monitoring systems warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 28 psi.

The manufacturers recommended correct inflation range is 26 psi to 30 psi. Assume the tires average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range?

(.4972 is not the correct answer)

Answer 1

ANSWER:

Given that,

µ =    28                              
σ =    3                              
we need to calculate probability for ,                                  
26   ≤ X ≤    30                          
X1 =    26   ,   X2 =   30                  
                                  
Z1 =   (X1 - µ ) / σ =   -0.667                        
Z2 =   (X2 - µ ) / σ =   0.667                          
                                  
P (   26   < X <    30   ) =    P (    -0.666666667   < Z <    0.667   )
                                  
= P ( Z <    0.667   ) - P ( Z <   -0.667   ) =    0.7475   -    0.2525   = 0.4950

The probability =0.4950

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