A major transportation company operates a fleet of trucks and it claims that the mean monthly maintenance cost per truck is different from $80. To test this hypothesis, a random sample of 20 trucks provided a sample mean  maintenance  cost  of  $74  with  a  sample  standard  deviation  of  $10.  Assume  that  the  monthly maintenance cost per truck is normally distributed.  

a. At a 2% level of significance, is there sufficient evidence to support the company’s claim?   

b. The  manager  is  also  interested  in  estimating  the  percentage  of  imported  trucks  in  the  current  fleet.  A sample of 40 trucks revealed 5 were imported. At a 5% level of significance, is there evidence that the true proportion of imported trucks exceeds 10%?

c. To  learn  the  work  satisfaction  of  her  drivers,  the  manager  also  wishes  to  estimate  proportion  of  truck drivers satisfied with their work within 10% of the true value 9 times out of 10. Determine the number of truck drivers that would have to be sampled.