A=length x width
A= 9cm x 8cm
A= 72cm
The probability of a binomial distribution with n trials is given by
![P(x)=^nC_x\cdot p^{n-x}\cdot q^x](https://tex.z-dn.net/?f=P%28x%29%3D%5EnC_x%5Ccdot%20p%5E%7Bn-x%7D%5Ccdot%20q%5Ex)
where, p is the probability of success and q = (1 - p) is the probability of failure.
Given n = 6 and p = 0.36, then q = 1 - 0.36 = 0.64
For x = 0,
![P(x)=P(0)=^6C_0(0.36)^6(0.64)^0=0.002](https://tex.z-dn.net/?f=P%28x%29%3DP%280%29%3D%5E6C_0%280.36%29%5E6%280.64%29%5E0%3D0.002)
For x = 1,
![P(x)=P(1)=^6C_1(0.36)^5(0.64)^1=6(0.00605)(0.64)=0.023](https://tex.z-dn.net/?f=P%28x%29%3DP%281%29%3D%5E6C_1%280.36%29%5E5%280.64%29%5E1%3D6%280.00605%29%280.64%29%3D0.023)
For x = 2,
![P(x)=P(2)=^6C_2(0.36)^4(0.64)^2=15(0.01680)(0.4096)=0.103](https://tex.z-dn.net/?f=P%28x%29%3DP%282%29%3D%5E6C_2%280.36%29%5E4%280.64%29%5E2%3D15%280.01680%29%280.4096%29%3D0.103)
For x = 3,
![P(x)=P(3)=^6C_3(0.36)^3(0.64)^3=20(0.046656)(0.262144)=0.245](https://tex.z-dn.net/?f=P%28x%29%3DP%283%29%3D%5E6C_3%280.36%29%5E3%280.64%29%5E3%3D20%280.046656%29%280.262144%29%3D0.245)
For x = 4,
![P(x)=P(4)=^6C_4(0.36)^2(0.64)^4=15(0.1296)(0.167772)=0.326](https://tex.z-dn.net/?f=P%28x%29%3DP%284%29%3D%5E6C_4%280.36%29%5E2%280.64%29%5E4%3D15%280.1296%29%280.167772%29%3D0.326)
For x = 5,
![P(x)=P(5)=^6C_5(0.36)^1(0.64)^5=6(0.36)(0.107374)=0.232](https://tex.z-dn.net/?f=P%28x%29%3DP%285%29%3D%5E6C_5%280.36%29%5E1%280.64%29%5E5%3D6%280.36%29%280.107374%29%3D0.232)
For x = 6,
![P(x)=P(6)=^6C_6(0.36)^0(0.64)^6=0.069](https://tex.z-dn.net/?f=P%28x%29%3DP%286%29%3D%5E6C_6%280.36%29%5E0%280.64%29%5E6%3D0.069)
Therefore, the binomial distribution table is as follows:
![\begin{center} \begin{tabular} {|c|c|c|c|c|c|c|c|} x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ [1ex] P(x) & 0.002 & 0.023 & 0.103 & 0.245 & 0.326 & 0.232 & 0.069 \end{tabular} \end{center}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%0A%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0Ax%20%26%200%20%26%201%20%26%202%20%26%203%20%26%204%20%26%205%20%26%206%20%5C%5C%20%5B1ex%5D%0AP%28x%29%20%26%200.002%20%26%200.023%20%26%200.103%20%26%200.245%20%26%200.326%20%26%200.232%20%26%200.069%0A%5Cend%7Btabular%7D%0A%5Cend%7Bcenter%7D)
Notice that the sum of the P(x) row is 1.
Answer: The expression would look like 2x+(25+3y).
Step-by-step explanation:
Let the number be x
2x+(25+3y)
Answer:
D
Step-by-step explanation:
choice A is not guaranteed since the values varied from 0 to 7.
choice B seems alright, but doesn't include about or anything about the long run.
choice C is incorrect because 50% are less than 3.12 and 50% are greater than 3.12.
choice D seems pretty good, since it says average, long run, approach, etc.
choice E is incorrect because it says "will be". It is not definite.