In a survey, 19 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $\$ 35.9$ and standard deviation of $\$ 14.5$. Estimate how much a typical parent would spend on their child's birthday gift (use a 90\% confidence level). Give your answers to 3 decimal places.
Express your answer in the format of $\bar{x} \pm$ Error.
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Step 1 ：Given that the survey results are roughly bell-shaped, we can use the z-score to estimate the mean amount spent on a child's birthday gift with a 90% confidence level.

Step 2 ：The formula for the confidence interval is \(\bar{x} \pm z \frac{\sigma}{\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(z\) is the z-score corresponding to the desired confidence level, \(\sigma\) is the standard deviation of the population, and \(n\) is the sample size.

Step 3 ：In this case, we have \(\bar{x} = \$ 35.9\), \(\sigma = \$ 14.5\), and \(n = 19\).

Step 4 ：We need to find the z-score for a 90% confidence level. This can be done using a z-table or a statistical calculator.

Step 5 ：Once we have the z-score, we can substitute these values into the formula to find the confidence interval.

Step 6 ：The error term for the confidence interval has been calculated as \$5.472.

Step 7 ：Finally, we can express the confidence interval in the format \(\bar{x} \pm\) Error.

Step 8 ：\(\boxed{\text{The estimated amount a typical parent would spend on their child's birthday gift, with a 90% confidence level, is \$35.9 \pm \$5.472.}}\)