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3. If X₁,..., X16 is a random sample from the normal distribution N(50, 100), determine

I

(x,-50)² ≤ 2630

(a) P 796.2 ≤

16

i=1

16

(b) P 854.7 ≤ (x,-X)² ≤ 2749

P ( 8547 ≤)

i=1

4. A consumer buys n light bulbs, each of which has a lifetime which is normally distributed.

around 800 hours with a standard deviation of 100 hours. A light bulb is replaced by another

as soon as it burns out. Assuming independence of the lifetimes, find the smallest n so that

the succession of light bulbs produces light for at least 10000 hours with probability 0.90.

Fig: 1