Help me please I don't understand

According to an article, 47% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly select

In-s [12.5K]

Answer:

a) $P(X=5)=(9C5)(0.47)^5 (1-0.47)^{9-5}=0.228$

b) $P(X=0)=(9C0)(0.47)^0 (1-0.47)^{9-0}=0.0033$

And replacing we got:

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

c) $P(X=4)=(9C4)(0.47)^4 (1-0.47)^{9-4}=0.257$

$P(X=5)=(9C5)(0.47)^5 (1-0.47)^{9-5}=0.228$

$P(X=6)=(9C6)(0.47)^6 (1-0.47)^{9-6}=0.135$

And adding we got:

$P(4 \leq X \leq 6)= 0.257+0.228+0.135=0.620$

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".

Solution to the problem

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

$X \sim Binom(n=9, p=0.47)$

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:

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

Assuming the following questions:

a. exactly five

For this case we can use the probability mass function and we got:

$P(X=5)=(9C5)(0.47)^5 (1-0.47)^{9-5}=0.228$

b. at least one

For this case we want this probability:

$P(X \geq 1)$

And we can use the complement rule and we got:

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

$P(X=0)=(9C0)(0.47)^0 (1-0.47)^{9-0}=0.0033$

And replacing we got:

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

c. between four and six, inclusive.

For this case we want this probability:

$P(4 \leq X \leq 6)$

$P(X=4)=(9C4)(0.47)^4 (1-0.47)^{9-4}=0.257$

$P(X=5)=(9C5)(0.47)^5 (1-0.47)^{9-5}=0.228$

$P(X=6)=(9C6)(0.47)^6 (1-0.47)^{9-6}=0.135$

And adding we got:

$P(4 \leq X \leq 6)= 0.257+0.228+0.135=0.620$

6 0

4 years ago

The image of the point (3, -4) under a translation is (0, –5). Find the coordinatesof the image of the point (8,7) under the sam

Sav [38]

We will have the following:

*First: We determine the translation rule:

We have that the point went from (3, -4) to (0, -5), thus the translation rule would be:

$(x,y)\to(x-3,x-1)$

Second: We apply the translation rule to the other point to determine it's image, that is:

$(8,7)\to(8-3,7-1)\to(5,6)$

So, the image of the second point is (5, 6).

6 0

1 year ago

Suppose the population of a certain city is 4251 thousand. It is expected to decrease to 3360 thousand in 50 years. Find the per

jonny [76]

Answer:

22.77%

Step-by-step explanation:

4351-3360 / 4351 x 100 = 22.77%

5 0

3 years ago

Gabriel used 1/3 of liter of milk to make 1/9 of jug of tea

Natalka [10]

So, it will take 1 liter of milk to make 1/3 jug of tea.

Also, it will take 3 liters of milk to make 1 jug of tea.

5 0

3 years ago

According to statistics, a person will devote 34 years to sleeping and watching TV. The number of years sleeping will exceed th

Kobotan [32]

Considering the definition of an equation and the way to solve it, a person will devote 28 years watching TV and 6 years sleeping.

<h3 /><h3>Definition of equation</h3>

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

When a value that is adding, when passing to the other member of the equation, it will subtract.
If a value you are subtracting goes to the other side of the equation by adding.
When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.
If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

Being "x" the number of years watching TV, and knowing that:

The number of years sleeping will exceed the number of years watching TV by 22.
A person will devote 34 years to sleeping and watching TV.

the equation in this case is:

x + (x+22) =34

Solving:

x + x =34 -22

2x= 12

x= 12 ÷ 2

As the number of years sleeping will exceed the number of years watching TV by 22, then<u><em> x +22= 6 +22= 28 years.</em></u>

Finally, a person will devote 28 years watching TV and 6 years sleeping.

Learn more about equations:

brainly.com/question/4983716

brainly.com/question/13314678

#SPJ1

3 0

2 years ago