The lifetimes of a particular type of light bulbs are approximately normally dis

Question

The lifetimes of a particular type of light bulbs are approximately normally distributed with a mean of 1200 hours and a standard deviation of 140 hours. A. Find the probability that a randomly chosen bulb will burn longer than 1400 hours. B. Find the probability that a randomly chosen bulb will last between 1000 and 1050 hours. C. Find the probability that a randomly chosen bulb will last no longer than 1060 hours. D. Find the probability that a randomly chosen bulb will last no longer than 920 hours. E. Twenty percent of the light bulbs have a lifetime of less than what value? F. Ten percent of the light bulbs have a lifetime of greater than what value?

Explanation / Answer

a) P(X>1400)

= P(Z>(1400-1200)/140)

= 0.0766

b) P(1000<X<1050)

= P(1000-1200)/140<Z<(1050-1200)/140)

= 0.0654

c) P(X<1060)

= P(Z<(1060-1200)/140)

= 0.1587

d) P(X<920)

= P(Z<(920-1200)/140)

= 0.0228

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