An environmental agency worries that many cars may be violating clean air emissions standards. the agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 3% and 90% confidence. to gauge the size of the problem, the agency first picks 40 cars and finds 8 with faulty emissions systems. how many should be sampled for a full investigation?

  482 cars

Step-by-step explanation:

The formula to find the sample size is given by :-

, where p is the prior estimate of population proportion.

= Two-tailed z-value for (significance level).

E= Margin of error .

Given : Margin of error = 3% = 0.03

Confidence level = 90%=0.90

By z-value table :

To gauge the size of the problem, the agency first picks 40 cars and finds 8 with faulty emissions systems.

Then , the prior estimate of population proportion of  faulty emissions systems =

Then, the required sample size would be :

Hence, 482 cars should be sampled for a full investigation.