Defining Your Triangles

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

3 years ago

HELP FAST PLEASE!!!

Alisiya [41]

Answer:

$y = -0.75x + 9.5$

Step-by-step explanation:

Equation of a circle is given as :

$(x-a)^{2} + (y-b)^2 = r^{2} \\(x-6)^{2} + (y-5)^2 = 4^{2}\\x^{2} - 12x + 36 + y^{2} -10y + 25 = 16\\x^{2} - 12x + y^{2} -10y + 45 = 0\\$

Take the derivative of the above with respect to x

$2x - 12 + 2y dy/dx - 10 dy/dy = 0\\\frac{dx}{dy} = \frac{6 - x}{y-5} \\At (2,8) dy/dx = (6-2)/(8-5) = 4/3\\dy/dx = 4/3\\The slope of the tangent to the circle, m = \frac{-1}{dy/dx} \\m = \frac{-1}{4/3}\\m= -0.75$

The equation of the tangent is given by :

$y - y_{1} = m(x - x_{1})\\ y - 8 = -0.75(x - 2)\\y - 8 = -0.75x + 1.5\\y = -0.75x + 9.5$

8 0

3 years ago

Read 2 more answers

corey’s campus store has $4,000 of inventory on hand at the beginning of the month. during the month, the company buys $41,000 o

Scrat [10]

If Corey’s campus store has $4,000 of inventory on hand at the beginning of the month. during the month, the company buys $41,000 of merchandise and sells merchandise that had cost $30,000. at the end of the month, $13,000 of inventory is on hand. how much shrinkage occurred during the month will be $2,000

Beginning inventory on hand $4,000

Add purchase $41,000

Cost of goods sold $45,000

Less Ending Merchandise sold ($30,000)

Less Ending Inventory on hand ($13,000)

Shrinkage $2,000

Inconclusion if Corey’s campus store has $4,000 of inventory on hand at the beginning of the month. during the month, the company buys $41,000 of merchandise and sells merchandise that had cost $30,000. at the end of the month, $13,000 of inventory is on hand. how much shrinkage occurred during the month will be $2,000

Learn more here:

brainly.com/question/18685380

6 0

3 years ago

I need help on my iready plz help me

vodomira [7]

Answer:

-3.5 meters per second

Step-by-step explanation:

Divide the distance by the time.

-17.5 meters / 5 seconds = -3.5 meters per second

8 0

3 years ago

Read 2 more answers

Which relationship in the triangle must be true?

forsale [732]

Answer:

sinB=cos(90-B)

Step-by-step explanation:

this is the relationship between sin and cos. other choices are wrong

3 0

3 years ago