10. In a recent study on world​ happiness, participants wereasked to evaluate their current lives on a scale from 0 to​ 10,where 0 represents the worst possible life and 10 represents thebest possible life. The responses were normally​distributed, with amean of 5.8 and a standard deviation of 2.3.
A. The probability that a randomly selected study​ participant'sresponse was less than 4 is __.
B.The probability that a randomly selected study​ participant'sresponse was between 4 and 6 is __.
C. The probability that a randomly selected study​ participant'sresponse was more than 8 is __.
​D.  Identify any unusual events. Explain yourreasoning. Choose the correct answer below.
A.The event in part left parenthesis a right parenthesis(a) isunusual because its probability is less than 0.05.
B.The events in parts left parenthesis a right parenthesis andleft parenthesis c right parenthesis(a) and (c) are unusual becausetheir probabilities are less than 0.05.
C. There are no unusual events because all the probabilities aregreaterThere are no unusual events because all the probabilitiesare greater than 0.05.
D. The events in parts left parenthesis a right parenthesiscomma left parenthesis b right parenthesis comma and leftparenthesis c right parenthesis are unusual because all of theirprobabilities areThe events in parts (a), (b), and (c) are unusualbecause all of their probabilities are less than 0.05.
11. Use the standard normal table to find the​ z-score thatcorresponds to the cumulative area 0.6312. If the area is not inthe​ table, use the entry closest to the area. If the area ishalfway between two​ entries, use the​ z-score halfway between thecorresponding​ z-scores.
z=__.
12. Use the standard normal table to find the​ z-score thatcorresponds to the given percentile. If the area is not in the​table, use the entry closest to the area. If the area is halfwaybetween two​ entries, use the​ z-score halfway between thecorresponding​ z-scores. If​ convenient, use technology to findthe​ z-score.
P15
The​ z-score that corresponds to P15 is __.
