Answer:
The mean of a sampling distribution of sample means is 87
The standard deviation of a sampling distribution of sample = 4
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called μx
- It is equal to the population mean μ
- The standard deviation of the distribution of sample means is
called σx
- The rule of σx = σ/√n , where σ is the standard deviation and n
is the size of the sample
* lets solve the problem
- A population has a mean (μ) is 87
∴ μ = 87
- A standard deviation of 24
∴ σ = 24
- A sampling distribution of sample means with sample size n = 36
∴ n = 36
∵ The mean of the distribution of sample means μx = μ
∵ μ = 87
∴ μx = 87
* The mean of a sampling distribution of sample means is 87
∵ The standard deviation of a sampling distribution of sample
means σx = σ/√n
∵ σ = 24 and n = 36
∴ σx = 24/√36 = 24/6 = 4
* The standard deviation of a sampling distribution of sample = 4
