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USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

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:

$X \sim Binom(n=4, p=1-0.25=0.75)$

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

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago

Quick answer please ddd

ikadub [295]

Answer:

C

Step-by-step explanation:

It makes the most sense.

4 0

3 years ago

Read 2 more answers

Help me plz help me

alukav5142 [94]

Answer:

1=3 given

1=2 vertical angles

3=4 vertical angles

2=4 transitive property (?)

Step-by-step explanation:

it's been a while since i've done proofs but i think this is right

4 0

3 years ago

Ronaldo can kick a soccer ball 35 meters per second which is about 80 mph. He kicked the ball from one end of the field to the o

professor190 [17]

Answer:

$t=3.142sec$

Step-by-step explanation:

From the question we are told that:

Speed of ball $V=35m/s\approx 80 mph$

Length of field $l=110m$

Generally the equation for Time taken $t$ is mathematically given by

$t=m/V$

$t=110/35$

$t=3.142sec$

$t \approx \frac{3.142}{60}$

$t \approx 0.05hrs$

Therefore it will take the ball to get from one end of the field to the other

$t=3.142sec$

3 0

3 years ago

Solve each inequality below. Represent the solutions on number lines. 7x − 2 < 3 + 2x

LekaFEV [45]

Hi, I would be glad to help you here.

<span>7x − 2 < 3 + 2x

Move terms

7x - 2x - 2 < 3

Collect the like terms

(7x - 2x) = 5x (<3 + 2 stays the same)

Calculate

5x (<3 + 2 = 5)

5x <5

Divide both sides of the inequality by (5) giving you,

x < 1

So, finally in a total the correct answer here is (x < 1)

</span>

6 0

3 years ago