To determine the mean battery life required for a smartphone to be in the top 15% of battery lives tested, we can use the properties of the normal distribution. We know that the battery life follows a normal distribution, and the cutoff for the top 15% is at least 45 hours.
1. **Identify the Z-score corresponding to the top 15%**:
The top 15% corresponds to the 85th percentile of the distribution (since the top 15% means that 85% of values