Question

1. the battery life of a new smartphone model is normally distributed, with a mean of 15.2 hours and a standard deviation of 1.3 hours. according to the empirical rule, approximately 95% of these smartphones have battery lives that are between ____ hours and ____ hours.

Explanation:

Step1: Recall the Empirical Rule

The Empirical Rule for a normal distribution states that approximately 95% of the data lies within 2 standard - deviations of the mean.

Step2: Calculate the lower bound

The formula for the lower bound is $\mu - 2\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 15.2$ hours and $\sigma=1.3$ hours. So, the lower bound is $15.2-2\times1.3=15.2 - 2.6 = 12.6$ hours.

Step3: Calculate the upper bound

The formula for the upper bound is $\mu + 2\sigma$. So, the upper bound is $15.2+2\times1.3=15.2 + 2.6 = 17.8$ hours.

Answer:

12.6, 17.8