Question 6 1 pts

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 11% of voters a

Radda [10]

Answer:

a) 0.0214 = 2.14% probability that none of the people are Independent.

b) 0.8516 = 85.16% probability that fewer than 6 are Independent.

c) 0.8914 = 89.14% probability that more than 2 people are Independent.

Step-by-step explanation:

For each people, there are only two possible outcomes. Either they are independent, or they are not. For each person asked, the probability of them being Independent voters is the same. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

It is believed that 11% of voters are Independent.

This means that $p = 0.11$

A survey asked 33 people to identify themselves as Democrat, Republican, or Independent.

This means that $n = 33$

A. What is the probability that none of the people are Independent?

This is P(X = 0). So

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

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

0.0214 = 2.14% probability that none of the people are Independent.

B. What is the probability that fewer than 6 are Independent?

This is

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

So

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

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X = 2) = C_{33,2}.(0.11)^{2}.(0.89)^{31} = 0.1724$

$P(X = 3) = C_{33,3}.(0.11)^{3}.(0.89)^{30} = 0.2202$

$P(X = 4) = C_{33,4}.(0.11)^{4}.(0.89)^{29} = 0.2041$

$P(X = 5) = C_{33,5}.(0.11)^{5}.(0.89)^{28} = 0.1463$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0214 + 0.0872 + 0.1724 + 0.2202 + 0.2041 + 0.1463 = 0.8516$

0.8516 = 85.16% probability that fewer than 6 are Independent.

C. What is the probability that more than 2 people are Independent?

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

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

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X < 2) = 0.0214 + 0.0872 = 0.1086$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1086 = 0.8914$

0.8914 = 89.14% probability that more than 2 people are Independent.

8 0

2 years ago

What is the next term in the sequence 58, 47, 36, 25, ...?<br> –58<br> –8<br> 14<br> 69

34kurt

The answer is 14
I hope this helps!

4 0

2 years ago

Read 2 more answers

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n

natali 33 [55]

Answer:

$f^{-1}=3ln_2(\frac{t}{100})$

f^-1 represents the number of hours the bacteria developed

Step-by-step explanation:

$f(t) = 100 \cdot 2^\frac{t}{3}$

To find inverse of a function , replace f(t) with y

$y= 100 \cdot 2^\frac{t}{3}$

replace t with y and y with x

$x= 100 \cdot 2^\frac{y}{3}$

solve for y

divide both sides by 100

$\frac{x}{100} =2^\frac{y}{3}$

take ln on both sides

$ln \frac{x}{100} =\frac{y}{3}ln 2$

divide both sides by ln

$ln_2(\frac{x}{100}) =\frac{y}{3}$

multiply by 3 on both sides

$y=3ln_2(\frac{x}{100})$

Replace x with t and y with f^-1

$f^{-1}=3ln_2(\frac{t}{100})$

f^-1 represents the number of hours the bacteria developed

7 0

2 years ago

Sally paid the following bills rent $450.00 cell phone $37.50 and cable $69.99 how much money did she pay ?

romanna [79]

Answer:

557.49

Step-by-step explanation:

Add the three bills together

450.00

37.50

69.99

--------------

557.49

3 0

2 years ago

In a group of 50 patrons, 18 patrons like lattes, 16 patrons like espressos, and 8 patrons like both coffee drinks. How many pat

Tcecarenko [31]

Add the 18, 16, and 8 together
Then subtract that number from 50.

18+16+8=42
50-42=8

So, 8 patrons don't like either.

3 0

2 years ago

Read 2 more answers