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moeshawashingto1
10.03.2020 •
Mathematics
The lifetime of lightbulbs that are advertised to last for 4000 hours are normally distributed with a mean of 4250 hours and a standard deviation of 300 hours. What is the probability that a bulb lasts longer than advertised
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Ответ:
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
and standard deviation
, the zscore of a measure X is given by:
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:
What is the probability that a bulb lasts longer than advertised?
This is 1 subtracted by the pvalue of Z when X = 4000. So
1 - 0.2033 = 0.7967
79.67% probability that a bulb lasts longer than advertised
Ответ:
x = 16
Step-by-step explanation:
2x + (3x-6) = 74
5x -6 = 74
5x = 74 + 6
5x = 80
x = 16