Question #3: (25 marks) Three hundred and sixty nurses randomly selected from th

Question

Question #3: (25 marks) Three hundred and sixty nurses randomly selected from the Rouge Valley Health System were rated either as "Below Average", "Average" or "Above Average" with respect to their nursing abilities. In addition, they were also rated with respect to their potential for advancement, "Fair", "Good or "Excellent". The results are as follows Potential For Advancement (Dependent Variable) Fair Good Excellent Total Nursing Ability (Independent Variable) Below Average (B1) Average (B2) Above Average (Ba) Total (A) (A2)(A) 40 101 230 135 360 60 69 105 120

Explanation / Answer

g)

i.

P(GW U GM) = P(GW) + P(GM) - P(GW U GM)

= 0.60 + 0.50 - 0.30

= 0.80 [ANSWER]

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ii.

P(GW U Gm)' = 1 - P(GW U GM)

= 1 - 0.80

= 0.20 [ANSWER]

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h)

P(all 10 are present) = (1-0.10)^10 = 0.34867844 [ANSWER]

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i)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    15      
p = the probability of a success =    0.4      
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   9   ) =    0.966166697
          
Thus, the probability of at least   10   successes is  
          
P(at least   10   ) =    0.033833303 [ANSWER]

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