Answer:
E. .10
Step-by-step explanation:
The standard deviation of sampling distribution of sample mean=σxbar=?
σxbar=σ/√n where, σ is the population standard deviation and n is sample size
We are given the population variance σ²=0.03 and we can calculate the population standard deviation from it by taking square root of variance
σ=√σ²
σ=√0.03
σ=0.1732
The standard deviation of sampling distribution of sample mean=σxbar=σ/√n
We are selecting 3 bolts so, n=3
σxbar=0.1732/√3
σxbar=0.1732/1.732
σxbar=0.1
So, The standard deviation of sampling distribution of sample mean is 0.1.
The standard deviation of the sampling distribution of the sample mean 0.10.
Given to us:
The average length is the mean, μ = 3;
Variance, v = 0.03;
Standard deviation,
[tex]\sigma = \sqrt{v} \\ \sigma = \sqrt{0.03} \\ \sigma = 0.1732[/tex];
we randomly select three bolts from this process, therefore
Sample size, n = 3;
The standard deviation of the sampling distribution of the sample mean,
[tex]\sigma_n= \dfrac{\sigma}{\sqrt{n}}\\\\\sigma_n= \dfrac{\00.1732}{\sqrt{3}}\\\\\sigma_n= \dfrac{\00.1732}{1.732}}\\\\\sigma_n= 0.10[/tex]
Hence, the standard deviation of the sampling distribution of the sample mean 0.10.
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