Instructions: Answer the following test items. Show your calculations as to how you get your answers, to get full credit for a correct answer. 1. Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in Table 5-5. Table5-5. Time Within Which Oil Was Washed off Reaction Within 5 Minutes After 5 Minutes Row Total None 420 50 470 Mild 60 330 390 Strong 20 120 140 Column Total 500 500 1000 Let's use the following notation for the various events: W-washing oil off within 5- minute, A-washing oil off after 5 minutes, N-no reaction, M-mild reaction, S-strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (a) (1) P(N) (ii) P(M) (iii) P(S) (b)(0) P(N/W) (ii) P(S/W) (e) () P(NA) (ii) P(SA) (d) (1) P(N and W) (ii) P(M and W) (c) (1) P(Nor M). (1) Are the events N=no reaction and M-mild reaction mutually exclusive? Explain. () Are the events N-no reaction and W-washing oil off within 5 minutes independent? Explain. 1. Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in Table 5-5. Table5-5. Time Within Which Oil Was Washed Off Reaction Within 5 Minutes After 5 Minutes Row Total None 420 50 470 Mild 60 330 390 Strong 20 120 140 Column Total 500 500 1000 Let's use the following notation for the various events: W-washing oil off within 5- minute, A-washing oil off after 5 minutes, N=no reaction, M=mild reaction, S=strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (a) (1) P(N) (ii) P(M) (iii) P(S) (b) (i) P(NW) the second part of question 1 (ii) P(S/W) (c)() P(NA) (ii) P(SA) (d) (1) P(N and W) (ii) P(M and W) (e) () P (Nor M). (1) Are the events N=no reaction and M=mild reaction mutually exclusive? Explain. () Are the events N=no reaction and W-washing oil off within 3 minutes independent? Explain
