Probability Question

Question

1. A database contains information on the wait times patients have reported in the emergency room to see a physician since the hospital opened 5 years ago. Suppose the wait times vary according to a normal distribution with mean wait time of 1.9 hours and a standard deviation of 0.7 hours. Based on a simple random sample of 23 patients at the hospital in the waiting room, what is the probability that they will have to wait for more than 2.5 hours

Answer 1

Need the z-score:

 

 z = (x - mean)/stddev 

    = (2.5 - 1.9)/0.7 

    = 0.6/0.7 

    = 6/7

    = 0.857142

 

On the normal curve, Prob ( z > 0.857142 ) = 

                                  1 - Prob(z<=0.857142) =

                                  1 - .7755

                                   = .2245

                                    = 22.45%