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GuDViN [60]
3 years ago
14

8 + 8( 8 - n ) = 40 + 8n

Mathematics
2 answers:
Ierofanga [76]3 years ago
7 0

n=2

8+8(8-n)=40+8n (distribute 8 through the parenthesis)

8+64-8n=40-8n (add the numbers)

<em>72-</em>8n=40+8n (move the variable to the left side and change its sign)

<em>72</em><em>-</em>8n+8n=40

-8n+8n=40<em>-72</em> (connect like terms)

-16n = -32 (divide both sides by -16)

<u><em>n=2</em></u>




irakobra [83]3 years ago
5 0

8 + 8(8 - n) = 40 + 8n

8 + 64 - 8n = 40 + 8n     <em>distributed 8 on the left side</em>

     72 - 8n = 40 + 8n      <em>added like terms on the left side</em>

     32 - 8n = 8n              <em>subtracted 40 from both sides</em>

     32        = 16n             <em>added 8n to both sides</em>

      2         =  n                <em>divided both sides by 2</em>

Answer: n = 2

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a) P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

b) P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

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Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=10, p=0.32)

The probability mass function for the Binomial distribution is given as:

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Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

Part b

P(X> 2)=1-P(X\leq 2)=1-[P(X=0)+P(X=1)+P(X=2)]

P(X=0)=(10C0)(0.32)^0 (1-0.32)^{10-0}=0.0211  

P(X=1)=(10C1)(0.32)^1 (1-0.32)^{10-1}=0.0995

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

Part c

P(2 \leq x \leq 5)=P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X=3)=(10C3)(0.32)^3 (1-0.32)^{10-3}=0.264

P(X=4)=(10C4)(0.32)^4 (1-0.32)^{10-4}=0.218

P(X=5)=(10C5)(0.32)^5 (1-0.32)^{10-5}=0.123

P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

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