Let
![X](https://tex.z-dn.net/?f=X)
denote the number of minutes spent brushing his teeth, and let
![\mu](https://tex.z-dn.net/?f=%5Cmu)
be the mean and
![\sigma](https://tex.z-dn.net/?f=%5Csigma)
the standard deviation for this distribution.
![\mathbb P(X](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3C1%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-%5Cmu%7D%5Csigma%3C%5Cdfrac%7B1-%5Cmu%7D%5Csigma%5Cright%29%3D0.40)
The z-score corresponding to this probability is approximately
![z=-0.2533](https://tex.z-dn.net/?f=z%3D-0.2533)
, which means
![\dfrac{1-\mu}\sigma=-0.2533\iff\mu-0.2533\sigma=1](https://tex.z-dn.net/?f=%5Cdfrac%7B1-%5Cmu%7D%5Csigma%3D-0.2533%5Ciff%5Cmu-0.2533%5Csigma%3D1)
Next, (note the sign change)
![\mathbb P(X>2)=0.02\implies\mathbb P(X\le2)=\mathbb P\left(\dfrac{X-\mu}\sigma\le\dfrac{2-\mu}\sigma\right)=0.98](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3E2%29%3D0.02%5Cimplies%5Cmathbb%20P%28X%5Cle2%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-%5Cmu%7D%5Csigma%5Cle%5Cdfrac%7B2-%5Cmu%7D%5Csigma%5Cright%29%3D0.98)
The corresponding z-score is approximately
![z=2.0538](https://tex.z-dn.net/?f=z%3D2.0538)
, so you have
![\dfrac{2-\mu}\sigma=2.0538\iff\mu+2.0538\sigma=2](https://tex.z-dn.net/?f=%5Cdfrac%7B2-%5Cmu%7D%5Csigma%3D2.0538%5Ciff%5Cmu%2B2.0538%5Csigma%3D2)
Solving the two equations for
![\mu](https://tex.z-dn.net/?f=%5Cmu)
and
![\sigma](https://tex.z-dn.net/?f=%5Csigma)
, you'll find that the mean is approximately
![\mu=1.1098](https://tex.z-dn.net/?f=%5Cmu%3D1.1098)
and the standard deviation is approximately
![\sigma=0.4334](https://tex.z-dn.net/?f=%5Csigma%3D0.4334)
.
Not sure but prob d. because the rest r short or don’t correlate
Answer:
12,000 m³
Step-by-step explanation:
- Area of it's base = 900 m²
- Height of the pyramid = 40 m
The volume of a pyramid = 1/3 × area of base × height
= 1/3 × 900 × 40
= 300 × 40
= 12,000 m³
I hope this helps answer your question.
Answer: <em>0=75degrees</em>
<u><em>Have a Great Day/Night</em></u>