At an auto parts place, the inspection time for a vehicle is approximately normally distributed with...
At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 30 minutes and the standard deviation 2 minutes.
1. What is the probability that a randomly selected car’s inspection time is between 25 minutes and 33 minutes? Round your answer to three decimal places.
2. The owner of this auto parts place will give a gift card to a customer if his car takes more 95% of inspection times. What is the required inspection time to get a gift card? Round your answer to two decimal places.
3. This place also offers free car wash to each car. The average car wash time is 10 minutes and the standard deviation is 2 minutes. What are the mean and variance of total {inspection and cleaning} time. Assume that the inspection time and car wash time are independent.
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