Step 1 :The problem is asking for a 94% confidence interval for the average incubation period of the novel coronavirus. The sample size is 45, the sample mean is 6.2 days, and the population standard deviation is 1.7 days.
Step 2 :The formula for a 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 level of confidence, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.
Step 3 :The Z-score for a 94% confidence interval can be found using a Z-table or a calculator that can compute probabilities for the standard normal distribution. The Z-score that corresponds to a 94% confidence interval is approximately 1.88.
Step 4 :Substitute the given values into the formula: sample_mean = 6.2, population_std_dev = 1.7, sample_size = 45, z_score = 1.88.
Step 5 :Calculate the standard error: standard_error = 0.2534210374499761
Step 6 :Calculate the margin of error: margin_of_error = 0.4764315504059551
Step 7 :Calculate the confidence interval: confidence_interval = (5.723568449594045, 6.6764315504059555)
Step 8 :The 94% confidence interval for the average incubation period of the novel coronavirus is approximately \(\boxed{(5.72, 6.68)}\) days.