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3 years ago

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Mathematics

2 answers:

Crank3 years ago

7 0

Answer:

21. x = 5, 23.

Step-by-step explanation:

I have researched on a reliable source however it is against brainlys terms of community guidelines to put that information in here.

☹️...........................................this is random but ya

Viefleur [7K]3 years ago

6 0

Answer:

21. x = 5, 23.

Step-by-step explanation:

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A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed

torisob [31]

Answer:

a) $P(X=14)=(20C14)(0.8)^{14} (1-0.8)^{20-14}=0.109$

b) $P(X\geq 10) = 1-P(X \leq 9) = 0.9994$

c) $P(X \leq 16)= 1-P(X>16) =1-P(X \geq 17)= 1- [P(X=17) +...+P(X=20)]=0.589$

d) $E(X)= np = 20 *0.8 = 16$

$Var(X) = np(1-p) = 20*0.8*(1-0.8) = 3.2$

Step-by-step explanation:

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".

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

$X \sim Binom(n=20, p=1-0.2=0.8)$

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

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

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

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

Part a

For this case we want this probability:

$P(X=14)$

And using the mass function we have this:

$P(X=14)=(20C14)(0.8)^{14} (1-0.8)^{20-14}=0.109$

Part b

For this case we want this probability:

$P(X \geq 10)$

And we can find this using the complement rule:

$P(X\geq 10) = 1-P(X$

$P(X=0)=(20C0)(0.8)^{0} (1-0.8)^{20-0}=1.05x10^{-14}$

$P(X=1)=(20C1)(0.8)^{1} (1-0.8)^{20-1}=8.39x10^{-13}$

$P(X=2)=(20C2)(0.8)^{2} (1-0.8)^{20-2}=3.19x10^{-11}$

$P(X=3)=(20C3)(0.8)^{3} (1-0.8)^{20-3}=7.65x10^{-10}$

$P(X=4)=(20C4)(0.8)^{4} (1-0.8)^{20-4}=1.30x10^{-8}$

$P(X=5)=(20C5)(0.8)^{5} (1-0.8)^{20-5}=1.66x10^{-7}$

$P(X=6)=(20C6)(0.8)^{6} (1-0.8)^{20-6}=1.66x10^{-6}$

$P(X=7)=(20C7)(0.8)^{7} (1-0.8)^{20-7}=1.33x10^{-5}$

$P(X=8)=(20C8)(0.8)^{8} (1-0.8)^{20-8}=8.65x10^{-5}$

$P(X=9)=(20C9)(0.8)^{9} (1-0.8)^{20-9}=0.00046$

And if we replace we got:

$P(X\geq 10) = 1-P(X \leq 9) = 0.9994$

Part c

For this case we want this probability:

$P(X \leq 16)$

And we can use the complement rule like this:

$P(X \leq 16)= 1-P(X>16) =1-P(X \geq 17)= 1- [P(X=17) +...+P(X=20)]$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.0576$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.0115$

And if we replace we got:

$P(X \leq 16)= 1-P(X>16) =1-P(X \geq 17)= 1- [P(X=17) +...+P(X=20)]=0.589$

Part d

The expected value is given by:

$E(X)= np = 20 *0.8 = 16$

$Var(X) = np(1-p) = 20*0.8*(1-0.8) = 3.2$

3 0

3 years ago

How do we name a minor arc?

erastova [34]

A minor arc (left figure) is an arc of a circle having measure less than or equal to ( radians). SEE ALSO: Arc, Major Arc, Semicircle.

7 0

3 years ago

What is the factor of 4x + 10

Mars2501 [29]

Answer:

2(2x + 5)

Step-by-step explanation:

2 is common to both 4x and 10, so 4x + 10 = 2(2x + 5)

7 0

3 years ago

Jet001 [13]

Answer:

5 because the 3 times 1000 and when you divide that it gets 5

4 0

3 years ago

The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was

arlik [135]

Answer: $163.85

Explanation:

1) Data:

Purchase price: $ 113.00

mark up: 45%

2) Formula

selling price = purchase price + mark up

mark up = % * purchase price

3) Solution

mark up = 45% * $ 113.00 = 0.45 * $ 113.00 = $50.85

selling price = $ 113.00 + $ 50.85 = $ 163.85

Answer: $ 163.85

5 0

3 years ago

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