Questions: Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=45 and σ=8; n=64

Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.

μ=45 and σ=8; n=64

Transcript text: Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. \[ \mu=45 \text { and } \sigma=8 ; n=64 \]

Solution

Solution Steps

Step 1: Formula for the standard deviation of the sampling distribution

The standard deviation of the sampling distribution of sample means (also known as the standard error) is given by the formula:

σ_x̄ = σ / √n

where σ is the population standard deviation and n is the sample size.

Step 2: Substitute the given values

In this problem, we are given σ = 8 and n = 64. Substituting these values into the formula:

σ_x̄ = 8 / √64

Step 3: Calculate the standard deviation

σ_x̄ = 8 / 8 σ_x̄ = 1

Final Answer: The final answer is $\boxed{1}$

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