Answer:
graph a
Step-by-step explanation:
Answer: see table below
<u>Step-by-step explanation:</u>
![\left\begin{array}{c|l}T&\qquad w(t)\\1&\dfrac{1}{1^2}=1\implies 1.00\\\\2&\dfrac{1}{2^2}=\dfrac{1}{4}\implies 0.25\\\\10&\dfrac{1}{10^2}=\dfrac{1}{100}\implies 0.01\\\\50&\dfrac{1}{50^2}=\dfrac{1}{2500}\implies 0.0004\\\\100&\dfrac{1}{100^2}=\dfrac{1}{10000}\implies 0.0001\\\\200&\dfrac{1}{200^2}=\dfrac{1}{40000}\implies 0.000025\\\\500&\dfrac{1}{500^2}=\dfrac{1}{250000}\implies 0.000004\\\\1000&\dfrac{1}{1000^2}=\dfrac{1}{100000}\implies 0.000001\\\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5Cbegin%7Barray%7D%7Bc%7Cl%7DT%26%5Cqquad%20w%28t%29%5C%5C1%26%5Cdfrac%7B1%7D%7B1%5E2%7D%3D1%5Cimplies%201.00%5C%5C%5C%5C2%26%5Cdfrac%7B1%7D%7B2%5E2%7D%3D%5Cdfrac%7B1%7D%7B4%7D%5Cimplies%200.25%5C%5C%5C%5C10%26%5Cdfrac%7B1%7D%7B10%5E2%7D%3D%5Cdfrac%7B1%7D%7B100%7D%5Cimplies%200.01%5C%5C%5C%5C50%26%5Cdfrac%7B1%7D%7B50%5E2%7D%3D%5Cdfrac%7B1%7D%7B2500%7D%5Cimplies%200.0004%5C%5C%5C%5C100%26%5Cdfrac%7B1%7D%7B100%5E2%7D%3D%5Cdfrac%7B1%7D%7B10000%7D%5Cimplies%200.0001%5C%5C%5C%5C200%26%5Cdfrac%7B1%7D%7B200%5E2%7D%3D%5Cdfrac%7B1%7D%7B40000%7D%5Cimplies%200.000025%5C%5C%5C%5C500%26%5Cdfrac%7B1%7D%7B500%5E2%7D%3D%5Cdfrac%7B1%7D%7B250000%7D%5Cimplies%200.000004%5C%5C%5C%5C1000%26%5Cdfrac%7B1%7D%7B1000%5E2%7D%3D%5Cdfrac%7B1%7D%7B100000%7D%5Cimplies%200.000001%5C%5C%5Cend%7Barray%7D%5Cright)
Answer:
The probability that the sample mean will lie within 2 values of μ is 0.9544.
Step-by-step explanation:
Here
- the sample size is given as 100
- the standard deviation is 10
The probability that the sample mean lies with 2 of the value of μ is given as
![P(| \bar{X}-\mu|](https://tex.z-dn.net/?f=P%28%7C%20%5Cbar%7BX%7D-%5Cmu%7C%3C2%29%5C%5CP%28-2%3C%5Cbar%7BX%7D-%5Cmu%3C2%29%5C%5C)
Here converting the values in z form gives
![P(-2](https://tex.z-dn.net/?f=P%28-2%3C%5Cbar%7BX%7D-%5Cmu%3C2%29%5C%5CP%28%5Cfrac%7B-2%7D%7B%5Cfrac%7B%5Csigma%7D%20%7B%5Csqrt%7Bn%7D%7D%7D%3C%5Cfrac%7B%5Cbar%7BX%7D-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%20%7B%5Csqrt%7Bn%7D%7D%7D%3C%5Cfrac%7B2%7D%7B%5Cfrac%7B%5Csigma%7D%20%7B%5Csqrt%7Bn%7D%7D%7D%29)
Substituting values
![P(-2](https://tex.z-dn.net/?f=P%28-2%3C%5Cbar%7BX%7D-%5Cmu%3C2%29%5C%5CP%28%5Cfrac%7B-2%7D%7B%5Cfrac%7B10%7D%20%7B%5Csqrt%7B100%7D%7D%7D%3Cz%3C%5Cfrac%7B2%7D%7B%5Cfrac%7B10%7D%20%7B%5Csqrt%7B100%7D%7D%7D%29%5C%5CP%28-2%3Cz%3C2%29%3DP%28z%3C2%29-P%28z%3C-2%29)
From z table
![P(z\leq 2)=0.9772\\P(z\leq -2)=0.0228\\P(-2\leq z\leq 2)=P(z\leq 2)-P(z\leq -2)\\P(-2\leq z\leq 2)=0.9772-0.0228\\P(-2\leq z\leq 2)=0.9544\\](https://tex.z-dn.net/?f=P%28z%5Cleq%202%29%3D0.9772%5C%5CP%28z%5Cleq%20-2%29%3D0.0228%5C%5CP%28-2%5Cleq%20z%5Cleq%202%29%3DP%28z%5Cleq%202%29-P%28z%5Cleq%20-2%29%5C%5CP%28-2%5Cleq%20z%5Cleq%202%29%3D0.9772-0.0228%5C%5CP%28-2%5Cleq%20z%5Cleq%202%29%3D0.9544%5C%5C)
So the probability that the sample mean will lie within 2 values of μ is 0.9544.