Answer:
option (D) 16.5
Step-by-step explanation:
Data provided:
Sleep time of , X = 15.9 is at the 10th percentile
Standard deviation, σ = 0.5 hour
also,
10th percentile of normal distribution is
Z = F⁻¹(0.10)
or
Z = - 1.28 (Using Standard Normal distribution)
Now,
![\\Z=\frac{X-\mu}{\sigma}](https://tex.z-dn.net/?f=%5C%5CZ%3D%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D)
or
X = μ + ( σ × Z )
or
μ = X - ( σ × Z )
on substituting the respective values, we get
μ = 15.9 - 0.5 × (-1.28)
or
μ = 16.5
Hence, the correct answer is option (D) 16.5
Answer:
Whats the percentage of the VAT?
Base = length * width.
We know that the base has an area of 10
And 60 is the volume. Then 60 / 10 = 6 Which is the height.
Distance formula between 2 points (x1,y1) and (x2,y2)
D=
![\sqrt{(x1-x2)^{2}+(y1-y2)^{2}}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28x1-x2%29%5E%7B2%7D%2B%28y1-y2%29%5E%7B2%7D%7D%20)
D=29 and one point is (-5,5) and the other is (k,0)
sub
29=
![\sqrt{(-5-k)^{2}+(5-0)^{2}}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28-5-k%29%5E%7B2%7D%2B%285-0%29%5E%7B2%7D%7D%20)
29=
![\sqrt{(-5-k)^{2}+(5)^{2}}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28-5-k%29%5E%7B2%7D%2B%285%29%5E%7B2%7D%7D%20)
square both sides
841=
![(-5-k)^{2}+(5)^{2}](https://tex.z-dn.net/?f=%20%28-5-k%29%5E%7B2%7D%2B%285%29%5E%7B2%7D%20)
841=
![(-5-k)^{2}+25](https://tex.z-dn.net/?f=%20%28-5-k%29%5E%7B2%7D%2B25%20)
minus 25 both sides
816=
![(-5-k)^{2}](https://tex.z-dn.net/?f=%20%28-5-k%29%5E%7B2%7D%20)
square root both sides don't forget positive and negative roots
+/-4√51=-5-k
add 5 to both sides
5+/-4√51=-k
times -1 both sides
-5+/-4√51=k
the possible values for k are
k=-5+4√51 or k=-5-4√51