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
Lapatulllka [165]
3 years ago
8

2. Suppose that you are looking for a student at your college who lives within five miles of you. You know that 55% of the 25,00

0 students do live within five miles of you. You randomly contact students from the college until one says he or she lives within five miles of you.
(a) What is the probability that you need to contact four people?

(b) How many students from the college you expect to contact until you find one lives within five miles of you?

(C) What is the standard deviation of the number of students to be contacted until one says who lives within five miles of you?

(d) Suppose you randomly ask 5 students at your college, what is the probability that 3 of them live within five miles of you?

(e) Suppose you randomly ask 5 students at your college, what is the expected number of students who live within five miles of you?​
Mathematics
1 answer:
Luden [163]3 years ago
6 0

Using the binomial distribution, it is found that:

a) There is a 0.0501 = 5.01% probability that you need to contact four people.

b) You expect to contact 1.82 students until you find one who lives within five miles of you.

c) The standard deviation is of 1.22 students.

d) 0.3369 = 33.69% probability that 3 of them live within five miles of you.

e) It is expected that 2.75 students live within five miles of you.

For each student, there are only two possible outcomes. Either they live within 5 miles of you, or they do not. The probability of a student living within 5 miles of you is independent of any other student, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 55% live within five miles, hence p = 0.55.

Item a:

This probability is P(X = 0) when n = 3(none of the first three) multiplied by 0.55(the fourth does live within five miles), hence:

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

P(X = 0) = C_{3,0}.(0.55)^{0}.(0.45)^{3} = 0.091125

p = 0.091125(0.55) = 0.0501

0.0501 = 5.01% probability that you need to contact four people.

Item b:

The expected number of trials in the binomial distribution until q successes is given by:

E = \frac{q}{p}

In this problem, p = 0.55, and 1 trial, thus q = 1, hence:

E = \frac{1}{0.55} = 1.82

You expect to contact 1.82 students until you find one who lives within five miles of you.

Item c:

The standard deviation of the number of trials until q successes are found is given by:

S = \frac{\sqrt{q(1 - p)}}{p}

Hence:

S = \frac{\sqrt{0.45}}{0.55} = 1.22

The standard deviation is of 1.22 students.

Item d:

This probability is <u>P(X = 3) when n = 5</u>, hence:

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

P(X = 3) = C_{5,3}.(0.55)^{3}.(0.45)^{2} = 0.3369

0.3369 = 33.69% probability that 3 of them live within five miles of you.

Item e:

The expected value of the binomial distribution is:

E(X) = np

Hence:

E(X) = 5(0.55) = 2,75

It is expected that 2.75 students live within five miles of you.

A similar problem is given at brainly.com/question/25343741

You might be interested in
Square root of 2 times 3 to the square root of 2
bija089 [108]

Answer:

6.68754...

Step-by-step explanation:

Assuming you mean:

\sqrt{2}\cdot 3^{\sqrt{2}}

5 0
3 years ago
Divide 72 in the ratio 7:2
Ksivusya [100]
Do you mean the ratio 1:2
6 0
3 years ago
How do you solve this answer for math -11/8
Alexxandr [17]

Answer:

-1.375

Step-by-step explanation:

7 0
3 years ago
A pizza parlor offers 10 toppings. How many 3-topping pizzas could they put on their menu? Assume double toppings are not allowe
andreev551 [17]

Using combination and permutation we found out that there are 30240 ways to make varieties of pizza with 3 toppings.

Given 10 toppings

10C3 =10!/3! 7! =120

10P5 =10!/5! =30240 ways

A permutation is a process of placing objects or numbers in order. Combining is the ability to select an object or number from a group of objects or collections such that the order of the objects does not matter.

In mathematics, a combination is the selection of elements from a set with different members, so the order of selection does not matter.

The process or state of binding. Some combination: A combination of ideas. Combined: A chord is a combination of notes. Alliance of Individuals or Parties: Combinations to restrict transactions.

Learn more about combination here: brainly.com/question/11732255

#SPJ4

8 0
1 year ago
Plz help will mark brainliest
Kryger [21]

∆ABC=∆DEF

AB=DE –>String

BC=EF–> Rib

m<C=m<F=90° –>List

AC=DF

So m<A=m<D=35 (It is not clear whether the number is 35 or 36, but the same number)

8 0
2 years ago
Other questions:
  • What is the fancy name (symbol) for the ratio of c/d?
    11·1 answer
  • What Is the midpoint of the line segment with endpoints (1, -6) and (-3, 4)?
    10·1 answer
  • what decimal point is between 1.5 and 1.7 and i know its 1.6 but on my homework it wont say 1.6 it says 1.625 , 1.25 , 1.75 , 1.
    11·1 answer
  • Please help me with this question
    11·1 answer
  • Lisa takes 3 hours to mow the lawn, while her cousin, Barb, takes 2 hours. How long will it take them working together? ​
    9·2 answers
  • If 4x plus 7 equals 18, what is the value of 12x plus 21
    7·1 answer
  • Carrie jared 13 liters of jam after 9 days. How much jam did Carriejar if she
    10·1 answer
  • Equation of line through (-3,7) with slope of 4 is?
    11·1 answer
  • What is 6.92x10^-3 written in standard form?
    13·1 answer
  • Question 17<br> - 3/6 + -3/6<br> =<br> O-6/14<br> O -7/8<br> O 6/24<br> O 9/14
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!