The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen.

Is it appropriate to use the normal approximation for the sampling distribution in this case? Why or Why not?

Was the "percent of fat calories that a person in America consumes each day" determined by this sample? If so, this sample is too small to generalize to the population.

If not, I would assume that the data was found with a larger sample and apply the normal distribution.

To determine whether it is appropriate to use the normal approximation for the sampling distribution in this case, we need to consider two factors: the sample size and the sampling distribution.

In this case, the sample size is 16 individuals. Generally, a sample size of at least 30 is considered large enough for the normal approximation to be valid. However, for the sampling distribution of the sample mean to be approximately normal, the underlying population distribution should also be normally distributed.

In this scenario, it is mentioned that the percent of fat calories consumed follows a normal distribution with a mean of 36 and a standard deviation of 10. Since the population distribution is already normal, the sample distribution of the sample mean will also be normal, regardless of the sample size. Therefore, it is appropriate to use the normal approximation for the sampling distribution in this case.

In summary, it is appropriate to use the normal approximation for the sampling distribution since the population distribution is already normal and the sample size is greater than 30.