your bills: In a large sample of customer accounts, a utllity company determined that the average number of days between when a bill was sent out and n the payment was made is 32 with a standard devlation of 6 days. Assume the data to be approximately bell-shaped. Part 1 of 3 (a) Estimate the percentage of bills for which payment was made in greater than 38 days.

To estimate the percentage of bills for which payment was made in greater than 38 days, we can use the properties of the normal distribution, given that the data is approximately bell-shaped. 1. **Calculate the z-score** for 38 days using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \(X\) is the value we are interested in (38 days), - \(\mu\) is the mean (32 days), - \(\sigma\) is the standard deviation (6 days). Plugging in the values: \[ z = \frac{(38 - 32)}{6} = \frac{6}{6} = 1 \] 2. **Look up the z-score** in the standard normal distribution table or use a calculator to find the area to the left of \(z = 1\). The area to the left of \(z = 1\) is approximately 0.8413, which means that about 84.13% of the bills are paid in 38 days or less. 3. **Calculate the percentage of bills paid in greater than 38 days**: \[ \text{Percentage paid in greater than 38 days} = 1 - \text{Percentage paid in 38 days or less} \] \[ = 1 - 0.8413 = 0.1587 \] To express this as a percentage: \[ 0.1587 \times 100 \approx 15.87\% \] Thus, approximately **15.87%** of the bills are paid in greater than 38 days.