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andre [41]
3 years ago
8

The lifetime of lightbulbs that are advertised to last for 4000 hours are normally distributed with a mean of 4250 hours and a s

tandard deviation of 300 hours. What is the probability that a bulb lasts longer than advertised
Mathematics
1 answer:
kobusy [5.1K]3 years ago
6 0

Answer:

79.67% probability that a bulb lasts longer than advertised

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 4250, \sigma = 300

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

This is 1 subtracted by the pvalue of Z when X = 4000. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{4000 - 4250}{300}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033

1 - 0.2033 = 0.7967

79.67% probability that a bulb lasts longer than advertised

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