Answer :
Answer:
a) [tex]\sigma = 0.4[/tex]
b) [tex]\sigma = 0.2[/tex]
Step-by-step explanation:
The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.
In this problem, we have that:
Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively. This means that [tex]\sigma = 1.6[/tex].
a.If X is the sample mean Young's modulus for a random sample of n = 16 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by
[tex]s = \frac{\sigma}{\sqrt{16}} = \frac{1.6}{4} = 0.4[/tex]
b. If X is the sample mean Young's modulus for a random sample of n = 64 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by
[tex]s = \frac{\sigma}{\sqrt{64}} = \frac{1.6}{8} = 0.2[/tex]