In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was

Complete question :

In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 4.5 and a standard deviation of 2.3. Answer parts (a)-(d) below.

(a) Find the probability that a randomly selected study participant's response was less than 4.

(b) Find the probability that a randomly selected study participant's response was between 4 and 6.

(c) Find the probability that a randomly selected study participant's response was more than 8.

1.) 0.4141

2.) 0.3288

3.) 0.0253

Step-by-step explanation:

Given a normal distribution :

Mean(m) = 4.5

Standard deviation (σ) = 2.3

A.) x < 4

Using :

Zscore = (4 - 4.5) / 2.3

Zscore = - 0.5 / 2.3

Zscore = - 0.2173913

P(Z < - 0.217) = 0.4141

B.) x between 4 and 6

From the above :

For x < 4;

P(Z < - 0.217) = 0.4141

For x < 6 ;

Using :

Zscore = (6 - 4.5) / 2.3

Zscore = 1.5 / 2.3

Zscore = 0.65217

P(Z < 0.65217) = 0.74285

0.74285 - 0.4141 = 0.3288

C.) X > 8

Using :

Zscore = (8 - 4.5) / 2.3

Zscore = 4.5 / 2.3

Zscore = 1.9565217

P(Z > 1.9565217 ) = 1 -P(Z < 1.9565217 )

P(Z < 1.9565217 ) = 0.9747

P(Z > 1.9565217 ) = 1 - 0.9747

= 0.0253

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24