Flextime is a term used to describe formalized flexible work

Flextime is a term used to describe formalized flexible working hours on the job. Many managers believe that flextime reduces worker tardiness, absenteeism, and turnover, and increases job satisfaction and performance. (Michigan State University Business Topics, Summer 1979). Assume that the distribution of job satisfaction ratings of all flextime workers has a population mean of m=35 and a standard deviation of s=10. Suppose a random sample of 35 flextime workers was taken and the job satisfaction rating was determined for each person in the sample. Calculate the following probability.

P(33 <X< 39 ) =

Solution

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    33      
x2 = upper bound =    39      
u = mean =    35      
n = sample size =    35      
s = standard deviation =    10      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u) * sqrt(n) / s =    -1.183215957      
z2 = upper z score = (x2 - u) * sqrt(n) / s =    2.366431913      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.118361785      
P(z < z2) =    0.991019761      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.872657976   [ANSWER]