Severe acute respiratory syndrome (SARS) is a viral respiratory illness. A random sample of 81 SARS patients was obtained, and researchers found that the mean incubation period was 4.6 days, with a standard deviation of 15.9 days. Determine the assumptions needed to construct a confidence interval for the mean incubation period of the SARS virus. Check all that apply (choose only three) population is normal $n p(1-p)>10$ the data is normal without outliers SRS $n<0.05 \mathrm{~N}$ $n>30$

Step 1 ：To construct a confidence interval for the mean incubation period of the SARS virus, we need to make certain assumptions. These assumptions are based on the Central Limit Theorem and the properties of the normal distribution.

Step 2 ：The first assumption is that the sample is a simple random sample (SRS). This means that every possible sample of size n has an equal chance of being selected.

Step 3 ：The second assumption is that the sample size is large enough. In practice, this often means that n > 30. This is because the Central Limit Theorem states that if the sample size is large enough, the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.

Step 4 ：The third assumption is that the population from which the sample is drawn is normally distributed. This is important because the confidence interval is based on the assumption that the sampling distribution of the mean is normal or nearly normal.

Step 5 ：The three assumptions needed to construct a confidence interval for the mean incubation period of the SARS virus are: the sample is a simple random sample (SRS), the sample size is large enough (n > 30), and the population is normally distributed.