The time needed to complete a final examination in a particu

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 83 minutes and a standard deviation of 13 minutes. Answer the following questions.

What is the probability of completing the exam in one hour or less (to 4 decimals)?
  

What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
  

Solution

a) What is the probability of completing the exam in one hour or less (to 4 decimals)?

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    60      
u = mean =    83      
          
s = standard deviation =    13      
          
Thus,          
          
z = (x - u) / s =    -1.769230769      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -1.769230769   ) =    0.038427686 [answer]

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b)

What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    60      
x2 = upper bound =    75      
u = mean =    83      
          
s = standard deviation =    13      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.769230769      
z2 = upper z score = (x2 - u) / s =    -0.615384615      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.038427686      
P(z < z2) =    0.269150375      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.230722689   [ANSWER]