Trucks that travel on highways have to stop at various locations to be weighed and inspected for safe brakes and light systems. Of these trucks, 76% are on interstate commerce while 24% are intrastate. Of the intrastate trucks, 3.4% are flagged for safety defects compared to 0.7% of those that are on interstate business. Complete parts a through c below. a. Calculate the probability that a randomly chosen truck is an interstate truck and is not flagged for a safety violation. The probability is nothing. (Round to three decimal places as needed.)
Accepted Solution
A:
Answer:The reuired probability is 0.756 Step-by-step explanation:Let the number of trucks be 'N'1) Trucks on interstate highway N'= 76% of N =0.76N2) Truck on intra-state highway N''= 24% of N = 0.24Ni) Number of trucks flagged on intrastate highway = 3.4% of N'' = [tex]\frac{3.4}{100}\times 0.24N=0.00816N[/tex]ii) Number of trucks flagged on interstate highway = 0.7% of N' = [tex]\frac{0.7}{100}\times 0.76N=0.00532N[/tex]Part a)The probability that the truck is an interstate truck and is not flagged for safety is [tex]P(E)=P_{1}\times (1-P_{2})[/tex]where[tex]P_{1}[/tex] is the probability that the truck chosen is on interstate[tex]P_{2}[/tex] is the probability that the truck chosen on interstate is flagged[tex]\therefore P(E)=0.76\times (1-0.00532)=0.756[/tex]