mrs. wilson placed the welcome mat shown below on her front door step. what is the area of her welcome mat in square feet?

In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre

Veseljchak [2.6K]

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that $p = 0.09$

41 people arrested for DUI in Illinois are selected at random.

This means that $n = 41$

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

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

$P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158$

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ .

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791$

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

$E(X) = np = 41*0.09 = 3.69$

d. What is the standard deviation of the number of repeat offenders?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83$

4 0

2 years ago

I need help with this problem right away please.

irga5000 [103]

Answer:

y= -1/9(x-1)^2 +2

Step-by-step explanation:

The vertex is at (1,2) and another point is at (-2,1).

We know the vertex form of a parabola is

y= a(x-h)^2 +k where (h,k) is the vertex

Substituting the vertex in

y= a(x-1)^2 +2

We have another point, (-2,1)

Substitue this in with x=-2 and y =1. This will let us find a

1 = a(-2-1)^2 +2

1 = a (-3)^2 +2

1 = a*9 +2

Subtract 2 from each side

1-2 = 9a +2-2

-1 = 9a

Divide by 9

-1/9 = 9a/9

-1/9 =a

Putting this back into the equation

y= -1/9(x-1)^2 +2

7 0

3 years ago

Brandon earns $6 for every shirt he sells. Which equation could Brandon use to determine the amount of money he earns (E) for an

BigorU [14]

I think it would D) E = 6 + s

7 0

3 years ago

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Where is the 90 degree angle?

Dovator [93]

Answer:

Step-by-step explanation:

A

3 0

2 years ago

If 10 + 5x is 12 more 8, what is the value of 3x?

vredina [299]

Answer:

3x=6

Step-by-step explanation:

10 + 5x =8+12

10 +5x = 20

Subtract 10 from each side

10-10+5x=20-10

5x= 10

Divide by 5

5x/5 = 10/5

x = 2

We want 3x

3(2) = 6

3x=6

5 0

3 years ago

Read 2 more answers