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 5.6 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.

 The probability that a randomly selected study participant's response was less than 4 is(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 (Round to four decimal places as needed.)

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

 The probability that a randomly selected study partcipant's response was more than 8 is . (Round to four decimal places as needed.)

 (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

 A. The events in parts (a), (b), and (c) are unusual because all of their probabiities are less than 0.05.

 B. There are no unusual events because all the probabilities are greater than 0.05.

 C. The events in parts (a) and (c) are unusual because their probablides are less than 0.05.

 D. The event in part (a) is unusual because its probability is less than 0.05.

Answer 1

Let X denotes the response score of a randomly selected study participant.

X ~ Normal(5.6, 2.3²)

a) The probability that a randomly selected study participant's score was less than 4

b) The probability that a randomly selected study participant's score was between 4 and 6 is

c) The probability that a randomly selected study participant's score was more than 8 is

d) ans-> B)