1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tensa zangetsu [6.8K]
3 years ago
6

There are several scenarios described below. For each of them, do the following (note: R.V. means random variable) (1) Define th

e R.V.--- that means something like, "Let X be the number of people who….." (2) Define the distribution and parameter(s) of the R.V. (3) Give the support of the R.V. (4) Write the probability statement related to the information being sought.
Mathematics
1 answer:
frutty [35]3 years ago
4 0

Answer:

a) The Ohio Bureau of Motor Vehicles states that 7 out of 8 people pass the written driver’s test.

Let X be the number of test given by the test taker to pass out.

So X~Geometric(p) where p=Probability that for a particular test anyone will pass the written test=7/8

and here support of X be equal to 1,2,3,..... i.e X is a Natural number

So ,probability that he will pass the written test in fewer than 4 tries

=P(X<4)

=\sum _{x=0}^{3}p(1-p)^{x-1}

b) LAIMO manufacturing company makes parts for the auto industry. Approximately 3% of the parts it makes are defective.

So let X=number of non defective parts sampled before the 3rd defective part is sampled

then X~Negative Binomial(r,p) where here r=3 and p=Probability that a randomly selected part is defective= 0.03

where support of X is {0,1,2,3,...}

So the probability that the third defective part is the 20th one sampled.

P(X=20-3=17)

=\binom{r+16}{17}p^r(1-p)^{16}

c) A BigMart store is going to hire 3 new cashiers. It has 18 applicants (10 male, 8 female) for these 3 cashier jobs.

So let X be number of female cashier appointed.

Here X~Hypergeometric(3,8,18) where

f(x)=P(X=x)

=\left\{\begin{matrix} \frac{\binom{8}{x}.\binom{10}{3-x}}{\binom{18}{3}} & ,x=0,1,2,3\\ 0 & ,otherwise \end{matrix}\right.

So the probability that none of the positions are filled by females

=P(X=0)

d) A gardener is inspecting the fall flowers in her garden. She notices, on average, 4 bugs on a flower. She randomly picks one flower from her garden.

Let X be the numbers of bugs on that flower

So X follows Poisson distribution with mean 4 where support of X is {0,1,2,3.....}

So the probability that the flower she picked has at least one bug on it

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

=1-e^{-4}\frac{4^x}{x!}|_{x=0}

e) A student is taking a true/false test that consists of 15 questions. Based on past performance the student has approximately a 70% chance of getting any individual question correct.

So let X be the number of questions that are correct among those 15 questions.

so X~Binomial(n,p) where n=15 and p=Probability that he get an individual question correct =0.7

where support of X be {0,1,2,3,...,15}

So the probability that the student gets at least 60% of the questions on the test correct or 15x60%=9 questions are correct

=P(X\geq9)

=\sum _{x=9}^{15}\binom{15}{x}p^x(1-p)^{15-x}

f) A certain radio station’s phone lines are busy approximately 95% of the time when trying to call during a contest.

Let X denotes the number of calls to get into the contest.

So X~Geometric(p) where p=Probability that in a call I get through into the contest=1-0.95=0.05

support of x={1,2,3,....}

So the probability that the 4 th time you call is the 1st time you get through during a contest.

=P(X=4)

=p(1-p)^4

You might be interested in
Which polynomial functions are written in
PolarNik [594]

Answer:

c and d

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Write the expressions in standard form. SHOW ALL STEPS! The sum of 9t – 13 and the opposite of 9t.
PSYCHO15rus [73]

Answer:

-13

Step-by-step explanation:

Opposite of 9t = -9t

Taking the sum of 9t - 13 and -9t

Sum = 9t - 13 + (-9t)

Sum = 9t - 13 - 9t

Sum = 9t-9t - 13

Sum  = -13

Hence the expression in standard form is -13

7 0
3 years ago
Somebody please prove if a triangle with side length of 6,8,10 is a right triangle using the Pythagorean theorem!! Will mark Bra
BabaBlast [244]
Answer:
Pythagorean’s theorem states that if a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the side lengths of the right triangle

Given that we can plug in
a= 6 , b = 8 , c = 10

We get an equation:

6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
5 0
3 years ago
Show me a graph that best represents the solution set to the system of a linear inequalities; y-x&gt;0. y-1&gt;0
tangare [24]
<h2>Answer:</h2>

The graph is shown in the attached image

4 0
3 years ago
Can someone help me with this math problem please?
Alexxandr [17]
First u have to find the square root for the number and then answer all of the root question then u have to find the angels
4 0
3 years ago
Read 2 more answers
Other questions:
  • Using the quadratic formula I can't remember what to do next <br>​
    13·1 answer
  • What fraction of a pound is forty pence
    8·2 answers
  • The the seats in the van are in pairs there are 16 seats How many pairs of seats are there
    8·2 answers
  • Marco has a collection of 437 bottles. Each month he buys 32 bottles .
    7·1 answer
  • Drag the tiles to the correct boxes to complete the pairs.
    15·1 answer
  • An urn contain 2 white marbles, 3 green marbles, and 5 red marbles. A marble is drawn and then replaced. Then a second marble is
    14·1 answer
  • Which measure of central tendency is the GREATEST?
    13·1 answer
  • Help me with this math question please I'm giving away brainliests​
    11·2 answers
  • Historically, the average diameter of the holes drilled has been 0.25 cm and the average range has been 0.10 cm. Samples of size
    11·1 answer
  • 20. Which expression is equal to 3(5x - 6) - 2(4x + 5)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!