Question

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.)

Answer 1

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 =0.76N

2) Truck on intra-state highway N''= 24% of N = 0.24N

i) Number of trucks flagged on intrastate highway  = 3.4% of N'' = $\frac{3.4}{100}\times 0.24N=0.00816N$

ii)  Number of trucks flagged on interstate highway  = 0.7% of N' = $\frac{0.7}{100}\times 0.76N=0.00532N$

Part a)

The probability that the truck is an interstate truck and is not flagged for safety is $P(E)=P_{1}\times (1-P_{2})$

where

$P_{1}$ is the probability that the truck chosen is on interstate

$P_{2}$ is the probability that the truck chosen on interstate is flagged

$\therefore P(E)=0.76\times (1-0.00532)=0.756$