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