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Sleep Stage Data Table Previous Sleep Stage Current Stage Non-REM REM Wake Non-REM 31,773 194 1,866 REM 369 7,635 170 Wake 1,668 306 5,281 Totals 33,810 8,135 7,317In a study, the various stages of sleep for a large group of people were monitored in 30-second intervals, or "epochs.\" For each epoch, sleep stage was categorized as Wake, REM, or Non-REM. The accompanying table provides a summary of the results. Each cell of the table gives the number of epochs that occurred when transitioning from the previous sleep stage to the current sleep stage. Complete parts a through e below. FF Click the icon to view the sleep stage data table. e. Are the events {previous stage is REM} and {current stage is Wake} independent? Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an integer or a decimal. Round to three decimal places as needed.) O A. Yes, because P({current stage is Wake} | {previous stage is REM})= and P(previous stage is REM) = B. No, because P({current stage is Wake} | {previous stage is REM})=| |and P(previous stage is REM) = ) C. No, because P({previous stage is REM} | {current stage is Wake})= and P(previous stage is REM) = O D. Yes, because P({previous stage is REM} | {current stage is Wake})= | and The most likely scenario for an accident for a natural gas pipeline is natural-gas leakage from a hole in the pipeline. The probability that the leak ignites immediately (I) causing a jet fire is 0.22. If the leak does not immediately ignite, it may result in the delayed ignition (D) of a gas cloud. If there is no delayed ignition, the gas cloud will disperse leak occurs in the natural-gas pipeline. harmlessly (H). Given no immediate ignition, the probability of delayed ignition causing a flash fire is 0.22. Suppose a The probability that either a jet fire or a flash fire will occuris 0.3916 . (Round to four decimal places as needed.) lllustrate with a tree diagram. Choose the correct answer below. O A. () B. Jet fire | Flash fire Outcome Jet fire Flash fire Outcome I*NH D(0.22) ~ INH I*ND IND O C. Jet fire Flash fire Outcome . INH IND I*NH IND The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. Complete parts a and b below. 5 o7 5 o P e o2 3 a. Suppose the sample points are equally likely. Find P(A) and P(B). PA)=] | PB)=| | (Round to two decimal places as needed.) 1 A fair coin is tossed three times, and the events A and B are defined as shown below. Complete parts a through d. A: {At least one tail is observed} B: {The number of tails observed is odd} P(B)= 5 (Type an integer or simplified fraction.) Find P(AUB). 7 : N : P(AUB) = 3 (Type an integer or simplified fraction.) Find P(A) . cy_ 1 . o : P(A ) =3 (Type an integer or simplified fraction.) Find P(ANB). P(ANB) = D (Type an integer or simplified fraction.) The effect of guilt emotion on how a decision maker focuses on a problem was investigated in a behavioral magazine A total of 176 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Inmediately after the task, students were presented with a decision problem where the stated option had predominantly negative features (spending money on repairing a very old car). The results (number responding in each category) are summarized in the accompanying table. Suppose one of the 176 participants is selected at random. Complete parts a through c. FFH Click the icon to view the table of chosen options and emotional states. The probability is 0.432 . (Round to three decimal places as needed.) c. Are the events {repair the car} and {guilty state} independent? First find the probability that the respondent chooses the stated option (repair the car). The probability is 0.330 . (Round to three decimal places as needed.) Now determine whether the events {repair the car} and {guilty state} are independent. Since the probability that the respondent chooses to repair the car is | the value found in part a, the events {repair the car} and {guilty state} Y| independent