Question

the mean life of a tire is 30,000 km. the standard deviation is 2000 km. then, 68% of all tires will have a life between __________ km and __________ km. 28,000 km and 32,000 km. 27,000 km and 31,000 km. 24,000 km and 34,000 km. 26,000 km and 34,000 km.

Explanation:

Step1: Apply the empirical rule

The empirical rule states that for a normal distribution, approximately 68% of the data lies within 1 standard deviation of the mean.

Step2: Calculate the lower bound

The lower bound is \(\mu-\sigma\), where \(\mu = 30000\) (mean) and \(\sigma=2000\) (standard deviation). So, \(30000 - 2000=28000\).

Step3: Calculate the upper bound

The upper bound is \(\mu+\sigma\). So, \(30000 + 2000 = 32000\).

Answer:

28,000 km and 32,000 km.