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

48 and 4

Explanation:

If we assume that
`\bar X` to be the random variable that proceed the normal distribution with mean
`\mu` and a standard deviation
`(\sigma )/(√(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 =
`(\sigma )/(√(n))`

standard deviation =
`(16 )/(√(16))`

standard deviation =
`(16)/(4)`

standard deviation = 4

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