Mathematics, 19.11.2019 00:31, chris858232

Consider a binomial experiment with n = 20 and p = .70. if you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations. compute f(12) (to 4 decimals). 0.1143 compute f(16) (to 4 decimals). 0.1304 compute p(x 16) (to 4 decimals). 0.2375 compute p(x 15) (to 4 decimals). 0.7624 compute e(x). 14

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answered: eric8020

Here are the results for the first 2 parts.

Step-by-step explanation:

f(x) = nCr p^r q^(n-r)

So f(12) = 20C12 (0.70^12 q^(0.30)^(20-12)

= 20C8 0.7^12 0.30^8

= 0.1144 .

f(16) = 0.1304.

answered: jaidencoolman2866

Step-by-step explanation:

The question is incomplete. p(x 16) is actually $P(X\geq 16)$ ; p(x 15) is actually $P(X\leq 15)$ and e(x) is E(X)

Wherever a random variable X can be modeled as a binomial random variable we write :

X ~ Bi (n,p)

Where ''n'' is the number of Bernoulli experiments taking place (whose variable is called binomial random variable).

And where ''p'' is the success probability.

In a Bernoulli experiment we define which event will be a ''success''

In order to calculate the probabilities for the variable X we can use the following equation :

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

Where '' P(X=x) '' is the probability of the variable X to assume the value x.

Where '' nCx '' is the combinatorial number define as :

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

In our question

X ~ Bi (20,0.70)

Now let's calculate the probabilities :

$f(12)=P(X=12)=(20C12).(0.70)^{12}.(1-0.70)^{20-12}=0.1144$

$f(16)=P(X=16)=(20C16).(0.70)^{16}.(1-0.70)^{20-16}=0.1304$ (I)

$P(X\geq 16)$ ⇒

$P(X\geq 16)=P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)$ (II)

$P(X=17)=(20C17).(0.70)^{17}.(1-0.70)^{20-17}=0.0716$ (III)

$P(X=18)=(20C18).(0.70)^{18}.(1-0.70)^{20-18}=0.0278$ (IV)

$P(X=19)=(20C19).(0.70)^{19}.(1-0.70)^{20-19}=0.0068$ (V)

$P(X=20)=(20C20).(0.70)^{20}.(1-0.70)^{20-20}=0.0008$ (VI)

Using (I), (III), (IV), (V) and (VI) in (II) :

$P(X\geq 16)=0.1304+0.0716+0.0278+0.0068+0.0008=0.2374$

Now :

$P(X\leq 15)$

$P(X\leq 15)=1-P(X\geq 16)$

$P(X\leq 15)=1-0.2374=0.7626$

Finally,

E(X)= μ (X)

E(X) is the mean of the variable X

In this case, X is a binomial random variable and its mean can be calculated as

E(X)=(n).(p)

In the question :

E(X)=(20).(0.70)=14

answered: Guest

water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3

answered: Guest

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice