SOLUTION: This is the socond problem I am struggling with. Any help would be appericated. thank you. 7.55 Tire pressure in a certain car is a normally distributed random variable with me

Question 142058: This is the socond problem I am struggling with. Any help would be appericated. thank you.
7.55 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. The manufacturer�s recommended correct inflation range is 28 psi to 32 psi. A motorist�s tire is inspected at random. (a) What is the probability that the tire�s inflation is within the recommended range? (b) What is the probability that the tire is under-inflated? *(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? (See The Wall Street Journal, July 14, 2004.)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
----
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) =
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