Question

If the sampled population has a mean of 48 and standard deviation of 16, then the mean and the standard deviation for the sampling distribution of x¯ for n = 16 are 4 and 1. 12 and 4. 48 and 4. 48 and 1. 48 and 16.

Answer 1

Answer:

48 and 4

Step-by-step explanation:

If we assume that $\bar X$ to be the random variable that proceed the normal distribution with mean $\mu$ and  a standard deviation $\dfrac{\sigma }{\sqrt{n}}$

Given that:

mean =48

standard deviation = 16

sample size = 16

The population mean is same as the population mean in sampling distribution that is 48.

The standard deviation of the sampling distribution is therefore calculated as:

standard deviation = $\dfrac{\sigma }{\sqrt{n}}$

standard deviation = $\dfrac{16 }{\sqrt{16}}$

standard deviation = $\frac{16}{4}$

standard deviation = 4

Thus; the mean and the standard deviation of the sampling distribution is 48 and 4