The mean and the standard deviation of the sampled population are, respectively, 77.4 and 4.0. find the mean and standard deviation of the sampling distribution of the sample mean x overbarx for samples of size n equals 225n=225. round your answers to one decimal place.

μₓ = 77.4

σₓ = 4.0

Step-by-step explanation:

We have to find the mean and standard deviation of the sampling distribution of the sample mean x, given mean and standard deviation of sampled population:

Mean=μ= 77.4

Standard deviation = σ = 4.0

and sample size = 255 n= 255 => n= 255/255 => n=1

so, the mean of sample mean x will be same as mean of the sampled population:

μₓ = μ = 77.4

and the standard deviation of sample mean x will be standard deviation of the sampled population divided by square root of sample size:

σₓ = σ / √ n

  = 4.0 / √1

  = 4.0

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