Question: In California, it is required by law to have your vehicle "smogged". Records indicate that 30% of vehicles do not pass their first time through the inspection. When this happens, the owner must take the vehicle to be repaired and then re-tested.

1. Let \(X\) be the random variable measuring the number of vehicles that fail the first time through. In a random sample of 50 vehicles, what is the expected value of the random variable \(X\) ?
2. What is the standard deviation of the random variable X?
3. A particular station failed 19 of the last 50 cars. This station has been suspected of failing more cars than would be expected on average. Based on the results from parts \(\mathrm{A}\) and \(\mathrm{B}\), does it seem unusual to have 19 cars fail the first time through?
4. In another random sample of inspections from various stations, what is the probability that at least 10 of the next 25 cars fail the first time through?

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document