Tire and automobile manufacturers and consumer safety experts all recommend that drivers maintain proper tire pressure in their cars. Consequently, many gas stations now provide air pumps and air gauges for their customers. In a Research Note (Nov. 2001), the National Highway Traffic Safety Administration studied the reliability of gas station air gauges. The next table gives the percentage of gas stations that provide air gauges that over report the pressure level in the tire.

a. If the gas station air pressure gauge reads 35 psi, what is the probability that the pressure is over reported by 6 psi or more?
b. If the gas station air pressure gauge reads 55 psi, what is the probability that the pressure is over reported by 8 psi or more?
c. If the gas station air pressure gauge reads 25 psi, what is the probability that the pressure is not over reported by 4 psi or more?
d. Are the events A = {over report by 4 psi or more) and B = (over report by 6 psi or more) mutually exclusive? Explain.
e. Based on your answer to part d, why do the probabilities in the table not sum to 1?

Transcribed Image Text:

Station Gauge Pressure Overreport Overreport by 4 psi or by 6 psi or More (%) Overrepot by 8 psi or More (96) More (96) 25 psi 35 psi 45 psi 55 psi 19 14