Answer:
<u></u>
- <u>a) P(X=1) = 0.302526</u>
- <u>b) P(X=5) = 0.010206</u>
- <u>c) P(X=3) = 0.18522</u>
- <u>d) P(X≤3) = 0.92953</u>
- <u>e) P(X≥5) = 0.010935</u>
- <u>f) P(X≤4) = 0.989065</u>
Explanation:
Binomial experiments are modeled by the formula:
![P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}](https://tex.z-dn.net/?f=P%28X%3Dx%29%3DC%28n%2Cx%29%5Ccdot%20p%5Ex%5Ccdot%20%281-p%29%5E%7B%28n-x%29%7D)
Where
- P(X=x) is the probability of exactly x successes
- p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.
- n is the number of trials
- 1 - p is the probability of fail
- there are only two possible outcomes for each trial: success or fail.
<u>a.) P (x=1)</u>
<u></u>
![P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526](https://tex.z-dn.net/?f=P%28X%3D1%29%3D%5Cdfrac%7B6%21%7D%7B1%21%5Ccdot%20%286-1%29%21%7D%5Ctimes%20%280.3%29%5E1%5Ctimes%281-0.3%29%5E%7B%286-1%29%7D%3D0.302526)
<u>b.) P (x=5)</u>
![P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206](https://tex.z-dn.net/?f=P%28X%3D5%29%3D%5Cdfrac%7B5%21%7D%7B5%21%5Ccdot%20%286-5%29%21%7D%5Ctimes%20%280.3%29%5E5%5Ctimes%20%281-0.3%29%5E%7B%286-5%29%7D%3D0.010206)
<u>c.) P (x=3)</u>
Using the same formula:
![P(X=3)=0.18522](https://tex.z-dn.net/?f=P%28X%3D3%29%3D0.18522)
<u>d.) P (x less than or equal to 3)</u>
- P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)
Also,
- P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)
You can use either of those approaches. The result is the same.
Using the second one:
- P(X=4) = 0.059335
- P(X=5) = 0.010206
- P(X=6) = 0.000729
- P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953
<u>e.) P(x greather than or equal to 5)</u>
- P(X≥5) = 0.010206 + 0.000729 = 0.010935
<u>f.) P(x less than or equal 4)</u>
- P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)
- P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065
<h3>
Answer: B) 74.5</h3>
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Explanation:
Average = (sum of scores)/(number of scores)
We can turn that equation into symbolic form to say
A = S/n
We're told that "18 students had an average of 80" (paraphrased) which means,
A = S/n
80 = S/18
80*18 = S
S = 1440
Those 18 students' scores add up to 1440.
For the other group of 40-18 = 22 students, their scores add to
S = A*n
S = 70*22
S = 1540
Overall, everyone's scores add up to 1440+1540 = 2980
Divide this over the number of people in class (40) to get the final answer
2980/40 = 74.5
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Here's an alternative way to compute the answer
(18/40)*80 + (22/40)*70 = 74.5
This works because 18/40 of the class got an average of 80 while the remaining 22/40 of the class got an average of 70.
I’m not sure but it’s either going to be b or c
Answer:
magnitude of a shown vector is
![4 \sqrt{5}](https://tex.z-dn.net/?f=4%20%5Csqrt%7B5%7D%20)