Answer: a. The proportion of the population is between 20 and 30 =0.2356
b. The probability that a randomly chosen value will be between 30 and 40 =0.4680
Step-by-step explanation:
Given : Mean : ![\mu=35](https://tex.z-dn.net/?f=%5Cmu%3D35)
Standard deviation : ![\sigma = 8](https://tex.z-dn.net/?f=%5Csigma%20%3D%208)
The formula to calculate z-score :-
![z=\dfrac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
For x= 20
![z=\dfrac{20-35}{8}=-1.875](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B20-35%7D%7B8%7D%3D-1.875)
For x= 30
![z=\dfrac{30-35}{8}=-0.625](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B30-35%7D%7B8%7D%3D-0.625)
For x= 40
![z=\dfrac{40-35}{8}=0.625](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B40-35%7D%7B8%7D%3D0.625)
a.
![P(20](https://tex.z-dn.net/?f=P%2820%3Cx%3C30%29%3DP%28-1.875%3Cz%3C-0.625%29%5C%5C%3D%20P%28-0.625%29-P%28-1.875%29%5C%5C%3D0.2659855-0.0303964%3D0.2355891%5Capprox0.2356)
b.
![P(30](https://tex.z-dn.net/?f=P%2830%3Cx%3C40%29%3DP%28-0.625%3Cz%3C0.625%29%5C%5C%3D%20P%280.625%29-P%280.625%29%5C%5C%3D0.7340144-0.2659855%3D0.4680289%5Capprox0.4680)
Each person will get 1/6 of the meatloaf because 1/3 of 1/2 is 1/6
Answer: Choice D ![(1-0.74)^4](https://tex.z-dn.net/?f=%281-0.74%29%5E4)
Reason:
74% = 0.74 represents the probability of him making any given free throw.
This means 1 - 0.74 is the probability of him missing.
Getting four misses in a row has a probability of (1-0.74)^4 which is the same as writing ![(1-0.74)^4](https://tex.z-dn.net/?f=%281-0.74%29%5E4)
In other words, we multiply exactly four copies of (1-0.74) to get our answer.
Answer: ![12\sqrt{2}\ in](https://tex.z-dn.net/?f=12%5Csqrt%7B2%7D%5C%20in)
Step-by-step explanation:
By definition a 45°, 45° and 90° is known as "Isosceles right triangle". This is an special type of triangle that has two congruent legs (which means that it has two legs that have equal length).
Then, for this case you need to use the following formula:
![L=\frac{1}{2}H\sqrt{2}](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B1%7D%7B2%7DH%5Csqrt%7B2%7D)
Where "L" is the length of any leg and "H" is the hypotenuse of the triangles.
In this case you know that:
![H=24\ in](https://tex.z-dn.net/?f=H%3D24%5C%20in)
Then, knowing the value of "H", you can substitute it into the formula and then you must evaluate in order to find the value of "L".
Therefore, you get the following result:
![L=\frac{1}{2}(24\ in)\sqrt{2}\\\\L=12\sqrt{2}\ in](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B1%7D%7B2%7D%2824%5C%20in%29%5Csqrt%7B2%7D%5C%5C%5C%5CL%3D12%5Csqrt%7B2%7D%5C%20in)