9x - 7x2 +4x2 - x + 4x3

An individual repeatedly attempts to pass a driving test. Suppose that the probability of passing the test with each attempt is

vladimir1956 [14]

Answer:

a) Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25

For this case the probability mass function would be given by:

$P(X= k) = (1-p)^{k-1} p , k = 1,2,3,...$

b) $P(X \leq 3) = P(X=1) +P(X=2) +P(X=3)$

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

And adding the values we got:

$P(X \leq 3) =0.25+0.1875+0.1406=0.578$

c) $P(X \geq 5) = 1-P(X$

And we can find the individual probabilities:

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

$P(X= 4) = (1-0.25)^{4-1} *0.25 = 0.1055$

$P(X \geq 5) = 1-[0.25+0.1875+0.1406+0.1055]= 0.316$

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

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

Let X the random variable that measures the number of trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

Part a

Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25

For this case the probability mass function would be given by:

$P(X= k) = (1-p)^{k-1} p , k = 1,2,3,...$

Part b

We want this probability:

$P(X \leq 3) = P(X=1) +P(X=2) +P(X=3)$

We find the individual probabilities like this:

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

And adding the values we got:

$P(X \leq 3) =0.25+0.1875+0.1406=0.578$

Part c

For this case we want this probability:

$P(X \geq 5)$

And we can use the complement rule like this:

$P(X \geq 5) = 1-P(X$

And we can find the individual probabilities:

$P(X= 1) = (1-0.25)^{1-1} *0.25 = 0.25$

$P(X= 2) = (1-0.25)^{2-1} *0.25 = 0.1875$

$P(X= 3) = (1-0.25)^{3-1} *0.25 = 0.1406$

$P(X= 4) = (1-0.25)^{4-1} *0.25 = 0.1055$

$P(X \geq 5) = 1-[0.25+0.1875+0.1406+0.1055]= 0.316$

3 0

3 years ago

Mr Floyd is laying grass squares in his backyard. He will cover the entire yard except for the vegetable garden. How many square

Alenkasestr [34]

Here we can first find the area of yard and then subtract the area of vegetable garden to get the required area.

The formula to find area is given by:

$A = l* w$

Now we find area of yard:

length is 25 ft and width is 15 ft.

$A = 25 * 15$

Area of yard = 375 ft²

Area of vegetable garden:

length = 8ft and width =8ft

So the vegetable garden is a square.

Area = 8*8

Area of vegetable garden =64 ft²

Area of backyard to be laid with grass = Area of yard-Area of vegetable garden

Area required = 375 -64 = 311 ft²

Answer : The area of backyard in which grass is to be laid is 311 square feet.

3 0

2 years ago

Read 2 more answers

Pls help me solve 5.a and 5.b

Tamiku [17]

You would add both totals since they said how much was the bill includingall the totals. So $192.77+ 48.19= 240.96
Since there is 12 people that need to chip in each, you would divide that total by 12.
240.96/12 = $20.08 each person would have to pay
Hope this helped!

3 0

2 years ago

I POSTED THIS QUESTION THREE TIMES IF YOU ANSWER THIS (CORRECTLY) GO ANSWER MY OTHER QUESTIONS JUST TO GET THE POINTS YOU DONT H

Charra [1.4K]

Answer:

12/3=4

Y= Time and X=The number of shoelaces

6 0

3 years ago

Read 2 more answers

Andre is paid $12 per hour at his caddying job and $9.50 per hour working at a local fast food restaurant. He would like to keep

Fynjy0 [20]

The equation that can be used to model this scenario is 12x + 9.5y ≥ 275 and x + y ≤ 25

Let x represents the number of hours Andre works at his caddying job and y represents the number of hours he works at the restaurant.

Since he earn at least $275.00 a week, hence:

12x + 9.5y ≥ 275 (1)

Also, he can work no more than 25 hours, hence:

x + y ≤ 25 (2)

Therefore the equation that can be used to model this scenario is 12x + 9.5y ≥ 275 and x + y ≤ 25

Find out more at: brainly.com/question/25285332

5 0

2 years ago

9x - 7x2 +4x2 - x + 4x3 - 3x2