The number of pages in a population of reports is normally d

The number of pages in a population of reports is normally distributed wit a mean of 38.2 pages and a standard deviation of 5.1 pages.

a. If a single report is randomly selected, find the probability that it is more than 50 pages long. Use formula and chart.

b. If a sample of 10 reports is randomly selected, find the probability that their mean length is more than 50 pages. Use your calculator. (Record the calculator command as well as the result.)

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    50      
u = mean =    38.2      
          
s = standard deviation =    5.1      
          
Thus,          
          
z = (x - u) / s =    2.31      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.31   ) =    0.010444077 [ANSWER]

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b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    50      
u = mean =    38.2      
n = sample size =    10      
s = standard deviation =    5.1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    7.32  
          
Thus, as this exceeds the limits of the table, we say          
          
P(z >   7.316642429   ) =    0 [VERY, VERY CLOSE TO 0]