Final answer:
When the sample size is sufficiently large, the sampling distribution of sample means can be approximated by a normal distribution. In this case, the sample size is n=16, which is smaller than the generally recommended size for a normal approximation. Therefore, a normal approximation may not be suitable. The standard deviation of the sampling distribution of sample means can be calculated using the formula: standard deviation = population standard deviation / square root of sample size.
Step-by-step explanation:
When the sample size is sufficiently large (usually considered to be greater than 30), the sampling distribution of the sample means can be approximated by a normal distribution, regardless of the shape of the population distribution. This is known as the Central Limit Theorem.
In this case, the sample size is n=16, which is smaller than the generally recommended size for a normal approximation. Therefore, a normal approximation may not be suitable for this particular sampling distribution.
To calculate the standard deviation of the sampling distribution of sample means, also known as the standard error of the mean, we can use the formula: standard deviation = population standard deviation / square root of sample size. This gives us: standard deviation = 10 / √16 = 10/4 = 2.5.