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

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

600,000,000,000, or 6e14

step-by-step explanation: