To solve this problem, we need to calculate the margin of error for a 90% confidence interval.

The margin of error (E) is given by the formula:

$E = z \times \frac{\sigma}{\sqrt{n}}$

Where:

• $z$ is the critical value corresponding to the 90% confidence level (we can find this from standard Z-tables),
• $\sigma$ is the standard deviation of the population,
• $n$ is the sample size.

Step 1: Find the critical value (z)

For a 90% confidence level, the z-value corresponding to the 90% confidence level is approximately 1.645 (this can be found in standard Z-tables or from statistical software).

Step 2: Plug values into the formula

• $\sigma = 13.5$
• $n = 40$

$E = 1.645 \times \frac{13.5}{\sqrt{40}}$

Now, let's calculate it.