# Question

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 underinflated?

*(c) A company 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?

(a) What is the probability that the tire's inflation is within the recommended range?

(b) What is the probability that the tire is underinflated?

*(c) A company 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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