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. Do not use PHStat2 for this question. You are allowed to use Standard Normal Distribution tables or Excel formula.
a. What is the probability that the tire's inflation is within the recommended range?
Show all the steps leading to your final answer.
b. What is the probability that the tire is under inflated? Show all the steps leading to your final answer.
c. A company has developed a microchip that will warn when a tire is 25% below the recommended mean, to warn of dangerously low tire pressure. How often would such an alarm be triggered? Show all the steps leading to your final answer.
Please show all work and cleary explain your answer for easy studying.