This can be solved by using the normal approximation to the binomial distribution.
mean = np = 10.000 * 0.5 = 5,000
The standard deviation is given by:
The probability of obtaining more than 5100 tails is 0.0228 and the probability of obtaining fewer than 5100 tails is 0.9772.
The odds of obtaining more than 5100 tails is therefore:
0.0228:0.9772 = 1:42.86.
Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Fundamental Theorem of Calculus 1]: 
Integration Property [Multiplied Constant]: 
U-Substitution
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:
- [<em>u</em>] Differentiate [Basic Power Rule, Derivative Properties]:
- [Bounds] Switch:
<u>Step 3: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Integral] U-Substitution:
- [Integral] Exponential Integration:
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
There are, 20475 different groups are possible if the manager wants to select one group of 4 people from his 28 assistants.
<h3>What is permutation and combination?</h3>
A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
A manager wants to select one group of 4 people from his 28 assistants.
The total number of groups possible = C(28, 4)
After calculating:
= 20475
Thus, there are, 20475 different groups are possible if the manager wants to select one group of 4 people from his 28 assistants.
Learn more about permutation and combination here:
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<span>If you have a $460,000 loan at 6% interest for 25 years; payments should be $2,963.79, not $2962.40. At $2,963.79, $2,300 would be interest, $663.79 would be principal. After that first payment your balance would be $459,336.21.
Hope I helped!!</span>
