Answer:
Yes, they are proportional
Step-by-step explanation:
First, simplify each fraction
30/80 can be simplified by dividing each number by 10
30/80
= 3/8
24/64 can be simplified by dividing each number by 8
24/64
= 3/8
So, each fraction will simplify to 3/8, meaning that they are proportional.
Answer:
8x + 7
Step-by-step explanation:
Answer:
((2^(-2))÷(3^3))^4=
Step-by-step explanation: expand
The value of 8 is in the hundred thousands
hope this helps
Using the binomial distribution, it is found that there is a 0.7215 = 72.15% probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated.
For each fatality, there are only two possible outcomes, either it involved an intoxicated driver, or it did not. The probability of a fatality involving an intoxicated driver is independent of any other fatality, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- 70% of fatalities involve an intoxicated driver, hence
.
- A sample of 15 fatalities is taken, hence
.
The probability is:
![P(10 \leq X \leq 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)](https://tex.z-dn.net/?f=P%2810%20%5Cleq%20X%20%5Cleq%2015%29%20%3D%20P%28X%20%3D%2010%29%20%2B%20P%28X%20%3D%2011%29%20%2B%20P%28X%20%3D%2012%29%20%2B%20P%28X%20%3D%2013%29%20%2B%20P%28X%20%3D%2014%29%20%2B%20P%28X%20%3D%2015%29)
Hence
![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)
![P(X = 10) = C_{15,10}.(0.7)^{10}.(0.3)^{5} = 0.2061](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%3D%20C_%7B15%2C10%7D.%280.7%29%5E%7B10%7D.%280.3%29%5E%7B5%7D%20%3D%200.2061)
![P(X = 11) = C_{15,11}.(0.7)^{11}.(0.3)^{4} = 0.2186](https://tex.z-dn.net/?f=P%28X%20%3D%2011%29%20%3D%20C_%7B15%2C11%7D.%280.7%29%5E%7B11%7D.%280.3%29%5E%7B4%7D%20%3D%200.2186)
![P(X = 12) = C_{15,12}.(0.7)^{12}.(0.3)^{3} = 0.1700](https://tex.z-dn.net/?f=P%28X%20%3D%2012%29%20%3D%20C_%7B15%2C12%7D.%280.7%29%5E%7B12%7D.%280.3%29%5E%7B3%7D%20%3D%200.1700)
![P(X = 13) = C_{15,13}.(0.7)^{13}.(0.3)^{2} = 0.0916](https://tex.z-dn.net/?f=P%28X%20%3D%2013%29%20%3D%20C_%7B15%2C13%7D.%280.7%29%5E%7B13%7D.%280.3%29%5E%7B2%7D%20%3D%200.0916)
![P(X = 14) = C_{15,14}.(0.7)^{14}.(0.3)^{1} = 0.0305](https://tex.z-dn.net/?f=P%28X%20%3D%2014%29%20%3D%20C_%7B15%2C14%7D.%280.7%29%5E%7B14%7D.%280.3%29%5E%7B1%7D%20%3D%200.0305)
![P(X = 15) = C_{15,15}.(0.7)^{15}.(0.3)^{0} = 0.0047](https://tex.z-dn.net/?f=P%28X%20%3D%2015%29%20%3D%20C_%7B15%2C15%7D.%280.7%29%5E%7B15%7D.%280.3%29%5E%7B0%7D%20%3D%200.0047)
Then:
![P(10 \leq X \leq 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.2061 + 0.2186 + 0.1700 + 0.0916 + 0.0305 + 0.0047 = 0.7215](https://tex.z-dn.net/?f=P%2810%20%5Cleq%20X%20%5Cleq%2015%29%20%3D%20P%28X%20%3D%2010%29%20%2B%20P%28X%20%3D%2011%29%20%2B%20P%28X%20%3D%2012%29%20%2B%20P%28X%20%3D%2013%29%20%2B%20P%28X%20%3D%2014%29%20%2B%20P%28X%20%3D%2015%29%20%3D%200.2061%20%2B%200.2186%20%2B%200.1700%20%2B%200.0916%20%2B%200.0305%20%2B%200.0047%20%3D%200.7215)
0.7215 = 72.15% probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated.
A similar problem is given at brainly.com/question/24863377