This problem requires the use of the empirical rule, which is applicable for bell-shaped (normal) distributions.

Key Information:

• Mean (μ) = 58
• Standard deviation (σ) = 5
• We are asked to find the approximate percentage of daily phone calls between 43 and 73.

Steps:

1. Find the Z-scores:

   • Convert the values 43 and 73 into Z-scores:
     • $Z = \frac{X - \mu}{\sigma}$
   • For 43: $Z_1 = \frac{43 - 58}{5} = \frac{-15}{5} = -3$
   • For 73: $Z_2 = \frac{73 - 58}{5} = \frac{15}{5} = 3$

2. Use the empirical rule:

   • The empirical rule states that:
     • 68% of the data falls within 1 standard deviation from the mean.
     • 95% of the data falls within 2 standard deviations from the mean.
     • 99.7% of the data falls within 3 standard deviations from the mean.

   Since 43 and 73 are 3 standard deviations away from the mean (on both sides), this range covers 99.7% of the distribution.

Thus, the approximate percentage of daily phone calls between 43 and 73 is 99.7%.

Would you like more details or have any further questions?

Here are 5 related questions:

1. What is the empirical rule and why is it important in statistics?
2. How do Z-scores help in understanding the normal distribution?
3. What percentage of data lies within 1 standard deviation in a normal distribution?
4. How would the result change if the range was between 48 and 68?
5. How can we use Z-scores to compare data from different distributions?

Tip: The empirical rule is most useful when dealing with normal distributions. It provides a quick estimate for data ranges without needing complex calculations.