1.A factory produces LED bulbs with an average lifespan of 52,000 hours and a standard deviation of 5000 hours.

A) What is the probability that a randomly selected bulb will last for less than 50,000 hours?

B) In a batch of 100,000 bulbs, how many do you expect to last for less than 50,000 hours? [Hint: this is a job for the Np shortcut! Be sure you understand why.]

C) What is the probability that a randomly selected LED bulb lasts between 51,000 and 53,150 hours?

D) The top 12% of bulbs last for at least how long?

E) The bottom 60% of bulbs will last for at most how long?

F) In a perfectly representative batch of 100,000 LED bulbs, how many last between 45,000 and 57,000 hours?

G) If it is known that a bulb has already lasted for 52,000 hours, what is the probability that it will last for at least 55,000 hours?