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 44.

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

Answer 1

SOLUTION:

From given data,

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.

Mean = = 5.8

Standard deviation = = 1.8

Z = (X - ) / = (X-5.8) / 1.8

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

P(X < 4) = P ((X - ) / < (4-5.8) / 1.8​​​​​​​)

P(X < 4) = P (Z < -1.8 / 1.8​​​​​​​)

P(X < 4) = P ( Z < -1 )

P(X < 4) = 0.15866

The probability that a randomly selected study​ participant's response was less than 4 is 0.15866.