Suppose that the lifetimes of light bulbs are approximately normally distributed

Question

Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following questions.

(a) What proportion of light bulbs will last more than 62 hours?

(b) What proportion of light bulbs will last 51 hours or less?

(c) What proportion of light bulbs will last between 59 and 62 hours?

(d) What is the probability that a randomly selected light bulb lasts less than 45 hours?

(Round to four decimal places as needed.)

Explanation / Answer

Mean = 57

Sd = 3.5

A) P(X > 62) = P(Z > (62 - 57)/3.5)

= P(Z > 1.43)

= 1 - P(Z < 1.43)

= 1 - 0.9236

= 0.0764

B) P(X < 51) = P(Z < (51 - 57)3.5)

= P(Z < - 1.71)

= 0.0436

C) P(59 < X < 62) = P((59 - 57)/3.5 < Z < (62 - 57)/3.5)

= P(0.57 < Z < 1.43)

= P(Z < 1.43) - P(Z < 0.57)

= 0.9236 - 0.7157

= 0.2079

D) P(X < 45) = P(Z < (45 - 57)3.5)

= P(Z < - 3.43)

= 0.0003

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