Mathematics, 06.10.2019 09:02 cpcoolestkid4

Apolice officer is using a radar device to check motorists’ speeds. prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?

Answers: 3

Show answers

Answers

Answer from: Yeetious

The probability is 0.8704

Step-by-step explanation:

A Binomial distribution apply when we have n identical and independent events with two possible results, success or fail, and a probability p of success and 1-p of fail. Then, the probability that from the n events, x are success is:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}$

Then, the number of motorist driving more than 5 miles per hour over the speed limit follow a Binomial Distributions, because we have 4 randomly selected motorists with two possible options: they are driving more than 5 miles per hour over the speed limit or they aren't, and the probability that they are driving more that 5 miles per hour over the speed is 0.4.

Finally, the probability P that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit is:

P = P(1) + P(2) + P(3) + P(4)

Where n is equal to 4 and p is equal to 0.4. Replacing the values for every x, we get:

$P(1)=\frac{4!}{1!(4-1)!}*0.4^{1}*(1-0.4)^{4-1}=0.3456$

$P(2)=\frac{4!}{2!(4-2)!}*0.4^{2}*(1-0.4)^{4-2}=0.3456$

$P(3)=\frac{4!}{3!(4-3)!}*0.4^{3}*(1-0.4)^{4-3}=0.1536$

$P(4)=\frac{4!}{4!(4-4)!}*0.4^{4}*(1-0.4)^{4-4}=0.0256$

Finally, P is equal to:

P = 0.3456 + 0.3456 + 0.1536 + 0.0256

P = 0.8704

Answer from: NeonPlaySword

The probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit is 0.8704.

Given :

Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit.

According to the Binomial distribution the probability is given by :

$\rm P(x) = \dfrac{n!}{x!(n-x)!}\times p^x \times (1-p)^{n-x}$

where n is the event and x is the success.

The probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit is:

$\rm P = P(1) + P(2) + P(3) + P(4)$

Here, n = 4 and P = 0.4.

$\rm P(1)= \dfrac{4!}{1!(4-1)!}\times 0.4^1 \times (1-0.4)^{4-1} = 0.3456$

$\rm P(2)= \dfrac{4!}{2!(4-2)!}\times 0.4^2 \times (1-0.4)^{4-2} = 0.3456$

$\rm P(3)= \dfrac{4!}{3!(4-3)!}\times 0.4^3 \times (1-0.4)^{4-3} = 0.1536$

$\rm P(4)= \dfrac{4!}{1!(4-4)!}\times 0.4^4 \times (1-0.4)^{4-4} = 0.0256$

Now, the value of P is given by:

$\rm P=P(1)+P(2)+P(3)+P(4)$

P = 0.3456 + 0.3456 + 0.1536 + 0.0256

P = 0.8704

For more information, refer to the link given below:

link

Answer from: Quest

Okay so it will be 1123
Which system of linear inequalities is represented by the graph? y > 2x – 1 and y < 2x + 2y

Answer from: Quest

d. 145*2 is 290 than the total angle is 360 then minus 290 then divide by two

Another question on Mathematics

Mathematics, 21.06.2019 14:30

The floor plan of a room has a scale of 2.5 in.: 35 ft. in the drawing, the length of the room is 8 in. and the width of the room is 6 in. what is the perimeter of the actual room?

Answers: 3

Answer

Mathematics, 21.06.2019 15:30

For one history test, keith had to answer 40 questions. of these 40 questions, keith answered 28 of them correctly. what percent did keith get on his history test? round your answer to the nearest tenth if necessary

Answers: 1

Answer

Mathematics, 21.06.2019 15:30

The weight of an object in a particular scale is 175.2 lbs. the measured weight may vary from the actual weight by at most 0.1 lbs. what is the range of actual weights of the object

Answers: 3

Answer

Mathematics, 21.06.2019 17:00

You have $600,000 saved for retirement. your account earns 5.5% interest. how much, to the nearest dollar, will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

Answers: 1

Answer

You know the right answer?

Apolice officer is using a radar device to check motorists’ speeds. prior to beginning the speed che...

Questions