Step-by-step explanation:

To construct a 90% confidence interval for the average number of kilometers a car is driven annually, we can use the formula:

Confidence Interval = x̄ ± Z * (σ / √n)

Where:

x̄ = sample mean

Z = Z-score corresponding to the desired confidence level (in this case, for a 90% confidence level, Z = 1.645)

σ = population standard deviation

n = sample size

Given:

x̄ = 13,500 km (sample mean)

σ = 900 km (population standard deviation)

n = 100 (sample size)

Plugging in the values into the formula, we have:

Confidence Interval = 13,500 ± 1.645 * (900 / √100)

Calculating the values inside the parentheses first:

900 / √100 = 900 / 10 = 90

Substituting the calculated value into the formula:

Confidence Interval = 13,500 ± 1.645 * 90

Calculating the values:

1.645 * 90 = 148.05 (rounded to two decimal places)

Therefore, the 90% confidence interval for the average number of kilometers a car is driven annually is:

13,500 ± 148.05

This can be written as:

(13,351.95, 13,648.05)

So, we can say with 90% confidence that the true average number of kilometers driven annually falls within the range of 13,351.95 km to 13,648.05 km.