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 5.8 and a standard deviation of 1.8.

Answer parts

​(a)dash–​(d)

below.

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

The probability that a randomly selected study​ participant's response was less than 4 is 0.1586.

​(Round to four decimal places as​ needed.)​

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

The probability that a randomly selected study​ participant's response was between 4 and 6 is

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	5.8
std deviation   =σ=	1.8000

probability that a randomly selected study​ participant's response was less than 4:

probability =

P(X<4)

=

P(Z<-1)=

0.1587

b) probability that a randomly selected study​ participant's response was between 4 and 6 :

probability =

P(4<X<6)

=

P(-1<Z<0.11)=

0.5438-0.1587=

0.3851

( please try 0.3856 if this comes wrong)