Answer:
NC = 7.7
C = 63.6°
T = 26.4°
Step-by-step explanation:
✔️Apply pythagorean theorem to find the length of NC:
NC = √(17.2² - 15.4²) = √58.68
NC ≈ 7.7
✔️Apply trigonometric function to find Angle T:
Reference angle = T
Hypotenuse = 17.2
Adjacent length = 15.4
Apply CAH, thus:
T ≈ 26.4°
✔️C = 180 - (90 + 26.4) (sum of triangle)
C = 63.6°
Answer:
And if we solve for a we got
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the hourly rates of a population, and for this case we know the distribution for X is given by:
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
