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**Chapter 5: Problem 6**

The lifetime of lightbulbs that are advertised to last for 3000 hours is normally distributed with a mean of 3700 hours and a standard deviation of 150 hours.

What is the probability that a bulb lasts longer than the advertised figure?

Answer :

Final answer:

Using the z-score formula, we find that the probability that a lightbulb will last longer than its advertised time is nearly 100%, because its lifespan is typically longer than advertised.

Explanation:

In the field of statistics, we deal with problems like these using a concept known as the z-score. The z-score measures the number of standard deviations an element is from the mean. The formula is z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. In this case, X = 3000 (the advertised time), μ = 3700 (the mean lifespan), and σ = 150 (the standard deviation).

Substituting these into the equation gives us z = (3000 - 3700) / 150 = -4.67. We refer to the z-table to find the corresponding probability, which is virtually zero. Hence, the probability that a bulb lasts less than the advertised time is virtually 100%. Because the question asks for the probability that it lasts longer than the advertised time, we subtract the above probability from 1, which gives us nearly 100%.

Learn more about Probability here:

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