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A new LED light to replace incandescent bulbs has come on the market. The box says...

Question

A new LED light to replace incandescent bulbs has come on the market. The box says...

A new LED light to replace incandescent bulbs has come on the market. The box says it has an average life of 8,000 hours with a standard deviation of 200 hours.

- What is the probability that a single bulb will last between 7950 and 8100 hours?

- What is the probability that the mean of a sample of 75 bulbs picked at random will be between 7950 and 8100 hours?

Answers

Solution :

Given that,

mean = \mu = 8000

standard deviation = \sigma = 200

\sigma\bar x = \sigma / \sqrt n = 200/ \sqrt 75 = 23.0940

= P[(7950 - 8000) /23.0940 < (\bar x - \mu \bar x) / \sigma \bar x < (8100 - 8000) /23.0940 )]

= P(-2.17 < Z < 4.33)

= P(Z < 4.33) - P(Z < -2.17)

= 1 - 0.0150

= 0.985

Probability = 0.985


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