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A car insurance company wanted information about the age of its customers. A random sample of 38 customers is selected, yielding a mean of 38.8 years and a standard deviation of 13.6 years. Find the upper confidence limit (UCL) of the 92% confidence interval for the population mean age. Round your answer to three decimal places.

Answer :

The upper confidence limit (UCL) of a 92% confidence interval for a sample of 38 customers with a mean age of 38.8 years and a standard deviation of 13.6 years is approximately 43.510.

To calculate the upper confidence limit (UCL) of a 92% confidence interval for the population mean age, we need to use the formula for the confidence interval, which involves the z-score, standard deviation, and sample mean.

The formula for the confidence interval is: Mean ± Z * (Standard Deviation/√n), where n is the sample size, and the Z value corresponds to the desired confidence level.

Given that the sample size n=38, the sample mean=38.8 years, and the standard deviation=13.6 years, we use the Z value for a 92% confidence level, which is approximately 1.75 (from the Z-table, or using your calculator's invNorm function). Plugging these values into our formula, we solve for the UCL as follows:

UCL = Mean + Z * (Standard Deviation/√n) = 38.8 + 1.75 * (13.6/√38),

After solving, we find that the upper confidence limit (UCL) equals 43.510, rounded to three decimal places.

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