A student takes a 20question exam The time that he needs to

A student takes a 20-question exam. The time that he needs to solve each problem is randomly distributed with mean of 5 minutes and standard deviation of 1.1 minute. What is the probability that he finishes the exam in less than 105 minutes 0.15 0.50 0.75 0.85

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    5.25      
u = mean =    5      
n = sample size =    20      
s = standard deviation =    1.1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.016394535      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.016394535   ) =    0.845279227 = 0.85 [ANSWER, D]