Question Suppose heights , in inches, of orangutans are normally distributed and have a known population standard deviation of 4 inches and an unknown population mean . A random sample of 16 orangutans is taken and gives a sample mean of 56 inches. Find the confidence interval for the population mean with a 95% confidence level. You may use a calculator or the common z values above. Round all numbers ; to three decimal places if necessary. Provide your answer below: (square ,square )

To find the confidence interval for the population mean with a 95% confidence level, we will use the sample mean, the population standard deviation, and the appropriate z-value for a 95% confidence level.Step 1: Identify the given information.The sample size (n) is 16.The population standard deviation (σ) is 4 inches.The sample mean ( ) is 56 inches.For a 95% confidence interval, the z-value ( ) is 1.960 (since 95% confidence level corresponds to a 2.5% significance level in each tail of the normal distribution).Step 2: Calculate the standard error of the mean (SEM).The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. Step 3: Calculate the margin of error (ME).The margin of error is calculated by multiplying the z-value by the standard error of the mean. Step 4: Calculate the confidence interval.The confidence interval is calculated by adding and subtracting the margin of error from the sample mean.Lower limit ( ) = Upper limit ( ) = Step 5: Round the results to three decimal places. Therefore, the 95% confidence interval for the population mean height of orangutans is approximately (54.040, 57.960) inches.**Accurate Answer**: The 95% confidence interval for the population mean is (54.040, 57.960) inches.