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Greeley [361]
3 years ago
8

5x680 in the Distributive property

Mathematics
1 answer:
AysviL [449]3 years ago
5 0
It is (5x600)+(5x80)=3400
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Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.
MrMuchimi
A random variable following a binomial distribution over n trials with success probability p has PMF

f_X(x)=\dbinom nxp^x(1-p)^{n-x}

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1

The mean is given by the expected value of the distribution,

\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}
\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}
\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}
\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}

The remaining sum has a summand which is the PMF of yet another binomial distribution with n-1 trials and the same success probability, so the sum is 1 and you're left with

\mathbb E(x)=np=126\times0.27=34.02

You can similarly derive the variance by computing \mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2, but I'll leave that as an exercise for you. You would find that \mathbb V(X)=np(1-p), so the variance here would be

\mathbb V(X)=125\times0.27\times0.73=24.8346

The standard deviation is just the square root of the variance, which is

\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834
7 0
3 years ago
Formula for a prism i am in need of help please help me
LenaWriter [7]
V=1/2a*c*h this is to solve the volume of a prism
4 0
2 years ago
pin Co. has $52,000 in its Cash account, $20,000 in its Inventory account, and $12,000 in its Notes Payable (short-term) account
KatRina [158]

Answer:

60000

Step-by-step explanation:

Assets - liabilities = share holder equity

(52,000+20,000)−12,000=60000

5 0
3 years ago
The Marrieds are planning to serve 380 guests at a breakfast event. They plan to serve tomato juice, which comes in 46 oz. cans.
Anna35 [415]
12 x 46 = 552
5 x 380 = 1900
552 x 3.44 = 1900
You will need 4 Cases
7 0
2 years ago
What is the median of the following list of numbers?
Novay_Z [31]

Answer:

The answer is 11.

Step-by-step explanation:

First, you put all of the numbers in order, from 7 - 19.

You find the median. You should get 11 and 11.

You add the numbers up to get 22 and divide by 2.

5 0
2 years ago
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