Question 142058
Tire pressure in a certain car is a normally distributed random variable with mean 30 psi (pounds per square inch) and standard deviation 2 psi.
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The manufacturer’s recommended correct inflation range is 28 psi to 32 psi. 
A motorist’s tire is inspected at random.
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(a) What is the probability that the tire’s inflation is within the recommended range? 
Find the z-value of 28 and or 32
z(28) = (28-30)/2 = -1 ; z(32)=(32-30)/2 = 1
P(28 < x < 32) = P(-1 < z < 32) = 6827
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(b) What is the probability that the tire is under-inflated)
P(x < 28) = P(z < -1) = 0.1587
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*(c) The Alliance of Automotive Manufacturers has developed a microchip that will warn when a tire is 25 percent below the recommended mean, to warn of dangerously low tire pressure. How often would such an alarm be triggered?
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25% below 30 is (3/4)30 = 22.5
z(22.5) = (22.5-30)/2 = -3.75
P(z < -3.75) = 0.00008844...
Cheers,
Stan H.
P(x<22.5) =