A recruitment agency has a list of 10 medical locums, labelled and listed in the following sample space S ={1,2,3,4,5,6,

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A recruitment agency has a list of 10 medical locums, labelled and listed in the following sample space S ={1,2,3,4,5,6,7,8,9,10). A total of 6 medical locums has already done shifts at Hospital A, they are listed in the set A={1,3,5,6,8,10}. A total of 3 medical locums has already done shifts at Hospital B, they are listed in the set B={2,5,10}. . . a) The CEO of the agency decides to draw a Venn diagram of the sample space. Identify the following 4 events by choosing the correct set of elements: Note: Marks will be subtracted for incorrect choices. {1,6,8} {1,3,6,8} {2} {4,7,9} o {5} {4,9} {5, 10} O AB AnB O O оооо O AnB 0 0 o O o AnB O
b) Calculate the probability that a medical locum has done shifts at least at one of the two hospitals, i.e. Hospital A or Hospital B. Round your answer to 1 decimal place. c) Events A and B are: o mutually exclusive since, P(ANB) + 0 O not mutually exclusive, since P(ANB) = 0 o not mutually exclusive since, P(ANB) + P(A). P(B) O not mutually exclusive since, P(ANB) = P(A). P(B) O mutually exclusive since, P(An B) = P(A). P(B) O mutually exclusive since, P(ANB) + P(A). P(B) o not mutually exclusive, since P(ANB) 0 O mutually exclusive since, P(An B) = 0
d) The number of hours that the locums work per week has a bell-shaped distribution with a mean of 24 and a standard deviation of 4 hours. . % o The percentage of locums that work: less than 16 hours per week is approximately: between 28 and 32 hours per week is approximately: % Round your answers to 3 decimal places. hours, it may be regarded as an outlier. If the number of hours that a medical locum work per week is more than S