The LifeSaver emergency helicopter service is available for

The LifeSaver emergency helicopter service is available for medical emergencies occurring between 15 and 90 miles from its base hospital. Emergencies that occur closer than 15 miles are more efficiently handled by the local ambulance service. A long term study of this service shows that the response time - T - (from dispatch to arrival on the scene) is a normally distributed variable with an average () of 46.00 minutes and a standard deviation () of 9.00 min. For each of the problems below, find the appropriate probability.

Obviously, the quicker the response time the more likely a patient is to survive. In fact, response times falling at or below the 5 percentile are accompanied by survival rates of 92 %. The response time that marks the 5 percentile is _____minutes

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.05      
          
Then, using table or technology,          
          
z =    -1.644853627      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    46      
z = the critical z score =    -1.644853627      
s = standard deviation =    9      
          
Then          
          
x = critical value =    31.19631736   [ANSWER]