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
Novay_Z [31]
3 years ago
8

A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they c

onclude that more than 60 percent of the city residents support the proposal. A survey of 2,000 randomly selected city residents will be conducted to investigate the level of support for the proposal. Let X represent the number of city residents in the sample who support the proposal. Assume that X is a binomial random variable.
Determine the mean and the standard deviation of the random variable X, assuming that 60 percent of city henudng proosal to create a new city park.
Mathematics
1 answer:
Paha777 [63]3 years ago
3 0

Answer:

The mean of the the random variable <em>X</em> is 1200.

The standard deviation of the random variable <em>X</em> is 21.91.

Step-by-step explanation:

The random variable <em>X</em> is defined as the number of city residents in the sample who support the proposal.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 2000 and <em>p</em> = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

  1. np ≥ 10
  2. n(1 - p) ≥ 10

Check the conditions as follows:

np=2000\times 0.60=1200>10\\\\n(1-p)=2000\times (1-0.60)=800>10  

Thus, a Normal approximation to binomial can be applied.

So,  the random variable <em>X</em> can be approximate by the Normal distribution .

Compute the mean of <em>X</em> as follows:

\mu=np

  =2000\times 0.60\\=1200

The mean of the the random variable <em>X</em> is 1200.

Compute the standard deviation of <em>X</em> as follows:

\sigma=\sqrt{np(1-p)}

  =\sqrt{2000\times 0.60\times (1-0.60)}\\=\sqrt{480}\\=21.9089\\\approx 21.91

The standard deviation of the random variable <em>X</em> is 21.91.

You might be interested in
Brian and Carlos are sharing a large sub sandwich. Brian ate 2 / 5 of the sandwich, and Carlos ate 1 / 5 of the sandwich. How mu
yKpoI14uk [10]

if I'm right it would be 2/5. you get your answer by adding 2/5 and 1/5 then subtract 5/5- 3/5 to get 2/5

8 0
3 years ago
Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.
alexandr1967 [171]

For the numbers in a+bi form, convert to polar form:


1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)

By DeMoivre's theorem,

(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i


-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)

\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i


\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)

\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)


For the numbers already in polar form, DeMoivre's theorem can be applied directly:


2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3


2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2


At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:


\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3

\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16

4 0
3 years ago
Starting time 2:15 elasped time 45 minutes
pshichka [43]
The answer is 3:00 LOL
7 0
2 years ago
How would I write a proportion for, “15% Of the toddlers in a preschool class drink water with their lunch. how many toddlers ar
ser-zykov [4K]
Let x be the number of toddlers.

0.15x=3

x=20
4 0
3 years ago
Right angle are known as the
marissa [1.9K]
Right angle are known as exactly 90 degrees corresponding to a quarter turn.
8 0
3 years ago
Read 2 more answers
Other questions:
  • I have 7 millions, 18 ten thousands, 2 hundreds, 10 tens, 1 one, 4 tenths, 15 hundredths what number am I
    7·1 answer
  • 5/3v = 125/7<br> PLEASE HELP
    12·1 answer
  • A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the functi
    10·2 answers
  • A family charges a trip to the zoo on a credit card. The simple interest rate is 12%. The charges are paid after 3 months. What
    11·1 answer
  • Find the area. Thank you!
    6·2 answers
  • Determine the type of correlation represented in the scatter plot below.
    12·2 answers
  • Dani bought a total of 8 pounds of peanuts and cashews. Peanuts, p, cost $2 per pound and cashews, c, cost $5 per pound. The tot
    14·1 answer
  • You can find the volume of a cylinder by using the equation
    5·1 answer
  • PLEASE HELP ME I WILL GIVE BRAINLIEST FOR THE RIGHT ANSWER
    7·1 answer
  • Who want 100 points?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!