## The mean life of a tire is 30,000 km. The standard deviation is 2000 km. 68% of all tires will have a life between___ km and ___km.

Question

The mean life of a tire is 30,000 km. The standard deviation is 2000 km. 68% of all tires will have a life between___ km and ___km.

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4 weeks 2021-09-24T00:01:08+00:00 1 Answer 0

68% of all tires will have a life between 28,000 km and 32,000 km.

Step-by-step explanation:

Given:

Mean life (μ) = 30,000 km

The standard deviation (σ) = 2000 km

The standard deviation of datasets which have normal distribution can be used to determine the proportion of values that lie within a particular range of the mean value. This follows Empirical rule:

68% of the values in the dataset will lie in area covered between Mean – 1 Standard Deviation and Mean + 1 Standard Deviation

Mean – 1 Standard Deviation = 30,000 -1(2000)= 30000-2000

Mean – 1 Standard Deviation = 28,000km

Mean + 1 Standard Deviation = 30000 + 1(2000) = 30000+2000

Mean + 1 Standard Deviation = 32,000km

68% of all tires will have a life between 28,000 km and 32,000 km.