Remainder of x^4+5x^3-2x^2+1/x^2+1

A population of red-bellied snakes is known to have a ratio of grey color morph to red color morph of 53:47. You wish to know th

Vsevolod [243]

Answer:

The probability is $P(X\leq 10)=0.093031581$

Step-by-step explanation:

We know that the ratio of grey color morph to red color morph is $53:47$

This can be written in terms of probability as :

$P(RedColorMorph)=\frac{47}{100}=0.47$

This means that the probability of obtain a red color morph snake in a random sample of 100 snakes is $0.47$ (If I only randomly select one snake).

Now, the number $X$ of red color morph snakes in a random sample ''n'' can be modeled as a binomial random variable. Where ''p'' is the success probability (In our case, the probability from obtain one red color morph snake out of 100 snakes) ⇒

$X:$ ''Number of red color morph snakes in the sample''

$p=0.47$

In our case, $n=30$

⇒ $X$ ~ Bi (n,p) ⇒ $X$ ~ Bi (30,0.47)

The probability function for $X$ is :

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

Where $nCx$ is the combinatorial number define as $nCx=\frac{n!}{x!(n-x)!}$ ⇒

$P(X=x)=(30Cx).(0.47)^{x}.(0.53)^{30-x}$

We need to calculate the probability of $P(X\leq 10)$

This probability is equal to :

$P(X\leq 10)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)$

For example,

$P(X=6)=(30C6).(0.47)^{6}.(0.53)^{24}=0.0015446$

We need to calculate all the terms of the sum and then calculate $P(X\leq 10)$

If we use any statistical program we will find that

$P(X\leq 10)=0.093031581$

7 0

3 years ago

In a certain town in the united states, 40% of the population are democrats and 60% are republicans. The municipal government ha

mixer [17]

Answer:

(a) 0.48, (b) 0.625, (c) 0.1923

Step-by-step explanation:

First define

Probability a person is a democrat: P(D) = 0.4

Probability a person is a republican: P(R) = 0.6

Probability a person support the measure given that the person is a democrat: P(SM | D) = 0.75

Probability a person support the measure given that the person is a republican: P(SM | R) = 0.3

Now for the Theorem of total probabilities we have

(a) P(SM) = P(SM | D)P(D)+P(SM | R)P(R) = (0.75)(0.4)+(0.3)(0.6) = 0.48

and for the Bayes' Formula we have

(b) P(D | SM) = P(SM | D)P(D)/[P(SM | D)P(D)+P(SM | R)P(R)] = (0.75)(0.4)/0.48 = 0.625

Now let SMc be the complement of support the measure, i.e.,

P(SMc | D) = 0.25 : Probability a person does not support the measure given that the person is a democrat

P(SMc | R) = 0.7: Probability a person does not support the measure given that the person is a republican,

and also for the Bayes' Formula we have

(c) P(D | SMc) = P(SMc | D)P(D)/[P(SMc | D)P(D)+P(SMc | R)P(R)] = (0.25)(0.4)/[(0.25)(0.4)+(0.7)(0.6)] = 0.1/(0.52)=0.1923

4 0

3 years ago

William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive. He wants each bag to

Elis [28]

Answer:

5 cans of veggies and 2 cans of fruit

8 0

3 years ago

What are the solutions to the following system?<br> -2x²+y=-5<br> y=-3x2+

Sphinxa [80]

Answer:

Simplifying

y = -0.4 + 0.6x

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not

disa [49]

Answer: b. False

Step-by-step explanation:

A dummy variable is a numerical variable used in regression analysis to represent values for categorical data by using value 0 (shows absence of particular category) or 1 (shows presence of particular category) .
We cannot use categorical data to evaluate the slope coefficient (numerical value) until we convert them into dummies.

Hence, the given statement is absolutely false.

4 0

3 years ago