prettylittlepixels
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- Nov 15, 2013
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57% of all Hobbits reside in the SAME province in which they were born. A sample of 19 Hobbits is randomly selected from the population. |
How many of the 19 Hobbits in the sample could be expected to be living in a province DIFFERENT from that in which they were born.
.43*19= 8.17, must be a whole number, so 8.
What is the standard deviation of this binomial probability function? |
[FONT=MathJax_Math]σ[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math]n[/FONT][FONT=MathJax_Math]p[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]p[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Size1]√[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]19[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]0.43[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]0.57[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Size1]√[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]2.16[/FONT][/FONT]
Using the binomial probability function:
P(x) = (binomial coefficient)(p)^x(q)^(n-x),
NOT THE NORMAL APPROXIMATION TO THE BINOMIAL, what is the probability that more than 7 of the 19 Hobbits reside in a province DIFFERENT from that in which they were born?
REMEMBER: p and x must be consistent with each other (they must both represent "success").
[P(0)+P(1)... P(7)] = 0.3564649998
1- 0.356464998= .6435350002
Am I done here with it rounded to 0.6435?
Would it be appropriate to use the normal approximation of the binomial to answer #3 above? Answer 1, 2, 3, or 4 below. | ||||||||||||||||||||||||||||||||||
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1. | Yes, because np and nq are both greater than or equal to 5. Because np= .43*19=8.17 and nq= .57*19= 10.83 |
USING THE NORMAL APPROXIMATION TO THE BINOMIAL (whether or not it is appropriate, use it), what is the probability that more than 7 of the 19 Hobbits reside in a province DIFFERENT from that in which they were born?
REMEMBER: p and x must be consistent with each other (they must both represent "success").
REMEMBER: The number of Hobbits is a discrete binomial so you must perform the continuity correction to approximate the probability using the normal distribution.
(7.5-8.17)/2.16= 0.3101851852
.31 on Z table is .1217
5-.1217= 4.8783
BUT BECAUSE THIS IS A PROBABILITY IT WOULD STILL BE .1217?
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