Answer:
a) 0.0476
b) 0.1471
c) 0.2252
d) 0.2275
e) 0.1706
f) 0.1013
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either they are defective, or they are not. This means that we solve this problem using the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinatios of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
In this problem we have that:
There are 100 bulbs, so
.
3% are defective, so
.
a) 0
![P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B100%2C0%7D.%280.03%29%5E%7B0%7D.%280.97%29%5E%7B100%7D%20%3D%200.0476)
b) 1
![P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B100%2C1%7D.%280.03%29%5E%7B1%7D.%280.97%29%5E%7B99%7D%20%3D%200.1471)
c) 2
![P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B100%2C2%7D.%280.03%29%5E%7B2%7D.%280.97%29%5E%7B98%7D%20%3D%200.2252)
d) 3
![P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B100%2C3%7D.%280.03%29%5E%7B3%7D.%280.97%29%5E%7B97%7D%20%3D%200.2275)
e) 4
![P(X = 4) = C_{100,4}.(0.03)^{4}.(0.97)^{96} = 0.1706](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B100%2C4%7D.%280.03%29%5E%7B4%7D.%280.97%29%5E%7B96%7D%20%3D%200.1706)
e) 5
![P(X = 5) = C_{100,5}.(0.03)^{5}.(0.97)^{95} = 0.1013](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B100%2C5%7D.%280.03%29%5E%7B5%7D.%280.97%29%5E%7B95%7D%20%3D%200.1013)
Step-by-step explanation:
the answer is 1,4 or 0,8 question answer
Answer:
180
Step-by-step explanation:
the angles in a triangle will always add up to 180º because 180º is equal to a straight/flat line.
I got u bud!
1 1/2-5/8= 7/8
just put 1 and 1/2 - 5/8 in your calculator, and you'll get this answer.
:D
Answer:No it is not proportional
Step-by-step explanation:
4 hours=$37
7 hours=$64.75
I t is not proportional because if 4 hours =$37 then 6 hours is supposed to be around $70 but 7 hours=$64.75