<u>650 cannonballs
</u>
Explanation step by step:
layer 12 is 12 ^ 2
<u>The formula is:
</u>
n * (n + 1) * (2n + 1) / 6
n = 12
12 (12 + 1) (2 * 12 + 1) / 6
12 * 13 * 25/6 =
650
<u>There are 650 cannonballs in this pyramid.</u>
Step-by-step explanation:
Let
. . . ,Xn be the random sample of n employee's sick days. It is given that the random samples follows the Normal distribution along with standard deviation of 7 days. Let
![X_i\sim N(\mu ,7)](https://tex.z-dn.net/?f=X_i%5Csim%20N%28%5Cmu%20%2C7%29)
![\bar{X} =\frac{1}{n}\Sigma X_i\sim N(\mu,\frac{7}{\sqrt n})](https://tex.z-dn.net/?f=%5Cbar%7BX%7D%20%3D%5Cfrac%7B1%7D%7Bn%7D%5CSigma%20X_i%5Csim%20N%28%5Cmu%2C%5Cfrac%7B7%7D%7B%5Csqrt%20n%7D%29)
or ![Z=\frac{\bar{X}-\mu}{7 /\sqrt n} \sim N(0,1)](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B%5Cbar%7BX%7D-%5Cmu%7D%7B7%20%2F%5Csqrt%20n%7D%20%5Csim%20N%280%2C1%29)
So,
![P(-Z_{\alpha /2} \leq Z\leq Z_{\alpha /2} ) = 1- \alpha](https://tex.z-dn.net/?f=P%28-Z_%7B%5Calpha%20%2F2%7D%20%5Cleq%20Z%5Cleq%20Z_%7B%5Calpha%20%2F2%7D%20%29%20%20%3D%201-%20%5Calpha)
![P(-Z_{\alpha /2} \leq \frac{\bar{X}- \mu}{7 / \sqrt n}\leq Z_{\alpha /2} ) = 1- \alpha](https://tex.z-dn.net/?f=P%28-Z_%7B%5Calpha%20%2F2%7D%20%5Cleq%20%5Cfrac%7B%5Cbar%7BX%7D-%20%5Cmu%7D%7B7%20%2F%20%5Csqrt%20n%7D%5Cleq%20Z_%7B%5Calpha%20%2F2%7D%20%29%20%20%3D%201-%20%5Calpha)
![P(\bar{X}-\frac{7}{\sqrt n} Z_{\alpha / 2} \leq \mu \leq \bar{X}+\frac{7}{\sqrt n} Z_{\alpha / 2} ) = 1- \alpha](https://tex.z-dn.net/?f=P%28%5Cbar%7BX%7D-%5Cfrac%7B7%7D%7B%5Csqrt%20n%7D%20Z_%7B%5Calpha%20%2F%202%7D%20%5Cleq%20%20%5Cmu%20%5Cleq%20%5Cbar%7BX%7D%2B%5Cfrac%7B7%7D%7B%5Csqrt%20n%7D%20Z_%7B%5Calpha%20%2F%202%7D%20%29%20%20%3D%201-%20%5Calpha)
Therefore, the confidence interval of the population mean for α = 0.05 is
= ![P(\bar{X}-\frac{7}{\sqrt n} Z_{\alpha / 2} , \bar{X}+\frac{7}{\sqrt n} Z_{\alpha / 2} )](https://tex.z-dn.net/?f=P%28%5Cbar%7BX%7D-%5Cfrac%7B7%7D%7B%5Csqrt%20n%7D%20Z_%7B%5Calpha%20%2F%202%7D%20%2C%20%5Cbar%7BX%7D%2B%5Cfrac%7B7%7D%7B%5Csqrt%20n%7D%20Z_%7B%5Calpha%20%2F%202%7D%20%29)
= ![P(21-\frac{7}{\sqrt 20} Z_{0.05 / 2} , 21+\frac{7}{\sqrt 20} Z_{0.05 / 2} )](https://tex.z-dn.net/?f=P%2821-%5Cfrac%7B7%7D%7B%5Csqrt%2020%7D%20Z_%7B0.05%20%2F%202%7D%20%2C%2021%2B%5Cfrac%7B7%7D%7B%5Csqrt%2020%7D%20Z_%7B0.05%20%2F%202%7D%20%29)
= (17.93, 24.07)
A=x(1+r/n)^nt
21150=x(1+0.032/12)^84
21150=x(1+0.0026666)^84
21150=x(1.002666666)^84
21150=x(1.25069809)
21150/1.25069809=x
16910.56=x
Hope this helps!