Question

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the target tire pressure of a certain car is 28 psi (pounds per square inch.)

(a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.)

When the tire pressure is (above or below?) (what?) psi

(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.)

Probability          

(c) The manufacturer’s 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? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability          

Answer 1

a)

.the target tire pressure of a certain car is 28 psi

28% below the target pressure = 0.28*28=7.84psi

TPMS trigger a warning for this car below (28-7.84)=20.16 psi

b)

µ =    28              
σ =    3              
left tailed                  
X ≤    20.16              
                  
Z =   (X - µ ) / σ =   -2.61          
                  
P(X ≤   20.16   ) = P(Z ≤   -2.61   ) =   0.004483
probability is 0.0045

c)

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
probability is 0.4950