Problem 2 The patient recovery time from a surgical procedur

(Problem 2) The patient recovery time from a surgical procedure is normally distributed with a mean of 5.3 days and standard deviation of 2.1 days. (5 points each, 10 points total) (a) What is the probability of spending more than 2 days in recovery after a surgical procedure? (b) What is the 90th percentile for recovery time after a surgical procedure?

Solution

a)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    2      
u = mean =    5.3      
          
s = standard deviation =    2.1      
          
Thus,          
          
z = (x - u) / s =    -1.571428571      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.571428571   ) =    0.941958433 [answer]

b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.9      
          
Then, using table or technology,          
          
z =    1.281551566      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    5.3      
z = the critical z score =    1.281551566      
s = standard deviation =    2.1      
          
Then          
          
x = critical value =    7.991258288   [answer]