question archive Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure
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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
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Answer:
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
