The times per week a student uses a lab computer are normall

The times per week a student uses a lab computer are normally distributed with a mean of 6.6 hours and a standred deviation of 1.1 hours. A student is randomly selected the fallowing probabilities Find the probability that the student uses computer less than 5 hour per week.

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    5      
u = mean =    6.6      
          
s = standard deviation =    1.1      
          
Thus,          
          
z = (x - u) / s =    -1.454545455      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.454545455   ) =    0.07289757 [ANSWER]

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B)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    6      
x2 = upper bound =    8      
u = mean =    6.6      
          
s = standard deviation =    1.1      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.545454545      
z2 = upper z score = (x2 - u) / s =    1.272727273      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.292720467      
P(z < z2) =    0.898442582      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.605722115   [ANSWER]

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C)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    9      
u = mean =    6.6      
          
s = standard deviation =    1.1      
          
Thus,          
          
z = (x - u) / s =    2.181818182      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.181818182   ) =    0.014561477 [ANSWER]