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 nomally distributed, with a mean of 4.6 and a standard deviation of 2.1. 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 rieeded.) (c) Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant'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. O A. The event in part (a) is unusual because its probability is less than 0.05. O B. There are no unusual events because all the probabilities are greater than 0.05 O C. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05. O D. The events in parts (a) and (c) are unusual because their probabilities are less than 0.05.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where O represents the worst possible life and 10 represents the best possible life. The responses were normally distributed,
with a mean of 4.6 and a standard deviation of 2.1. 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 rieeded.)
(c) Find the probability that a randomly selected study participant's response was more than 8.
The probability that a randomly selected study participant'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.
O A. The event in part (a) is unusual because its probability is less than 0.05.
O B. There are no unusual events because all the probabilities are greater than 0.05
O C. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.
O D. The events in parts (a) and (c) are unusual because their probabilities are less than 0.05.

Expert Solution

Step 1

Given that, 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 4.6 and a standard deviation of 2.1