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 25,000 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?

How to do this five questions ? thanks​

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) There is a 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

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item a:

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

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

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

[tex]p = 0.091125(0.55) = 0.0501[/tex]

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:

[tex]E = \frac{q}{p}[/tex]

In this problem, [tex]p = 0.55[/tex], and 1 trial, thus [tex]q = 1[/tex], hence:

[tex]E = \frac{1}{0.55} = 1.82[/tex]

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:

[tex]S = \frac{\sqrt{q(1 - p)}}{p}[/tex]

Hence, since [tex]q = 1, p = 0.55[/tex]:

[tex]S = \frac{\sqrt{0.45}}{0.55} = 1.22[/tex]

The standard deviation is of 1.22 students.

Item d:

This probability is [tex]P(X = 3)[/tex] when [tex]n = 5[/tex], hence:

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

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

There is a 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:

[tex]E(X) = np[/tex]

Hence, since [tex]n = 5, p = 0.55[/tex]:

[tex]E(X) = 5(0.55) = 2,75[/tex]

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

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

Here are two line segments with lengths e and f. Calculate the exact values of e and f. Which is larger? Use the Pythagorean Theorem: a^2 + b^2 = c^2

Five tickets numbered 1, 2, 3, 4, and 5 are placed in a box, and three are selected at random. Determine the probability of obtaining a 1 or a 2 or both.

SLOVE I GIVE BRAINLEST
18+ -27

A. -45

B. -9

C. 9

D. 48

A man is 32 years older than his son ten year ago he was three times as old as his son was then find the present age of each?

Pete worked 44 hours and 30 minutes on his new job. He makes $9.86 per hour. For each hour of overtime, he earns time and a half. How much will he earn for one week?

Find the missing number in the following series: __ 85 81 83 79 81 77

(5 1/4−2 1/2)+(6 2/3−3 1/2) plsss help (real answers)

What is the first step needed to solve 3 over 4 multiplied by x minus 3 equals negative 18 ? (1 point) a Add 3 to both sides b Subtract 18 from both sides c Multiply both sides by 3 d Divide both sides by 4

10
Find the area of the shape.
Either enter on exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.
units
Show Calculator

Round to 2 decimal places 0.966

Answers:
A. 113 cm^3
B. 141 cm^3
C. 565 cm^3
D. 126 cm^3

What is the answer to :
2x (4+3) -5 x [4-(9-7)]
??

Uhm is this a function?

Which of the functions below have period pie check all that apply

As a bonus question on a test, Mr. Smith wrote 8z + (5y6w). He told his students the values of each variable: w=6, y=2, and z = 7. What is the simplification of Mr. Smith's expression?​

if AB=12 cm and BC =13 cm then AC = 25 cm

Four times the product of a number x and a number y is equal to 20.

Only answer this if you know the answer.

Find The nth Term of this number sequence
18, 16, 14, 12

Both questions 7 and 8

Write an equation of a line with an x-coefficient of - 3 and a y-intercept of 7

a store pays $26 for a lamp. The store marks up the price by 40%. What is the amount of the markup

the area of a square is 36 centimeters. how long is each side of the square?

Terrence has 100 points out of 200 possible points in his Geometry class.
A. Determine his grade as a percentage and letter grade. Explain how you determined this.
B. Calculate how many more points Terrence needs to be passing. Explain how you calculated this.​

Would appreciate the help

Name the property of addition illustrated.

[3+(-8)] + 9 = 3+(- 8+9)

pls help i think its 3600 but i dont know NO EXPLANATION JUST ANSWER

50 points! don't answer if you don't know! Thank You
#1 Jeanne's bank account earns interest annually. The equation shows her starting balance of ​$200 and her balance at the end of five ​years, ​$267.65. At what rate r did Jeanne earn​ interest?
r= ​%
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)



#2 The volume of a soap bubble is 62.3mm^3 Find the radius and diameter of the soap bubble. Use 3.14 for pie.
The radius of the bubble is about mm.
​(Round to the nearest tenth as​ needed.)

STRUCTURE Tell whether the triangles are similar.

Jon wants to earn at least $75,000 a year and live in a posh urban setting. James’s career plan includes earnings of $35,000 a year and simple, cheap living conditions. Whose lifestyle expectations are better?

Both are equally valid, they just have different preferences.

James’s, because he has more realistic expectations.

Jon’s, because he will have a higher quality of life

It depends on their career goals and family plans.

I need help with number 5 please