Question

the batteries from a certain manufacturer have a mean lifetime of 860 hours, with a standard deviation of 70 hours. assuming that the lifetimes are normally distributed, complete the following statements. (a) approximately 99.7% of the batteries have lifetimes between 650 hours and 1070 hours. (b) approximately 68% of the batteries have lifetimes between hours and hours.

Explanation:

Step1: Recall the empirical rule for normal distribution

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

Step2: Calculate the lower bound

The lower bound is $\mu-\sigma$, where $\mu = 860$ (mean) and $\sigma = 70$ (standard deviation). So, $860 - 70=790$.

Step3: Calculate the upper bound

The upper bound is $\mu+\sigma$. So, $860 + 70 = 930$.

Answer:

790, 930