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The Acme Light Bulb Company claims that the lifetimes of its 100-Watt light bulbs follow a normal distribution with a mean of 325 hours and a standard deviation of 35 hours.

a) Find the probability that a randomly selected Acme 100-Watt light bulb will fail in less than 315 hours.

b) What lifetime corresponds to the 95th percentile?

b) A random sample of 50 light bulbs is taken. What is the probability that the sample mean lifetime is less than 315 hours?

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