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 2.4. Answer parts ​(a)dash​(d) below. ​(a) Find the probability that a randomly selected study​ participant's response was less than 4. (b) Find the probability that a​ participant's response was between 4 and 6. ​(c) Find the probability that a randomly selected study​ participant's response was more than 8. ​(d) Identify any unusual events. Explain your reasoning?

Answer 1

This is a normal distribution question with

a)

P(x < 4.0)=?

The z-score at x = 4.0 is,

z = -0.2083

This implies that

b)

P(4.0 < x < 6.0)=?

This implies that

P(4.0 < x < 6.0) = P(-0.2083 < z < 0.625) = P(Z < 0.625) - P(Z < -0.2083)

P(4.0 < x < 6.0) = 0.7340144709512995 - 0.4174973658227892

c)

P(x > 8.0)=?

The z-score at x = 8.0 is,

z = 1.4583

This implies that

P(x > 8.0) = P(z > 1.4583) = 1 - 0.927621064882385

d)

There is no unusual events because the probability in all the above cases are greater than 0.05

PS: you have to refer z score table to find the final probabilities.
Please hit thumps up if the answer helped you