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.

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.