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 2.2. 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 enter your response here. ​(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 enter your response here. ​(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​ participant's response was more than 8 is enter your response here. ​(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) and (c) are unusual because their probabilities are less than 0.05.   B. The event in part (a) is unusual because its probability is less than 0.05.   C. There are no unusual events because all the probabilities are greater than 0.05.   D. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.

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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
2.2.
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
enter your response here.
​(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
enter your response here.
​(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​ participant's response was more than
8
is
enter your response here.
​(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) and (c)
are unusual because their probabilities are less than 0.05.
 
B.
The event in part
(a)
is unusual because its probability is less than 0.05.
 
C.
There are no unusual events because all the probabilities are greater
than 0.05.
 
D.
The events in parts (a), (b), and (c) are unusual because all of their probabilities are
less
than 0.05.
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