The cost of ink cartridges for inkjet printers can be substantial over the life of a printer. Printer manufacturers publish the number of pages that can be printed from an ink cartridge in an effort to attract customers. HP claims that the CN045W black print cartridge (the most popular black ink cartridge from HP, according to Amazon) will yield an average of 2,300 pages. To test this claim, an independent lab measured the page count of 45 of these cartridges and found the average page count to be 2,267.5. Assume the standard deviation for this population is 210 pages.

a. Create a 95% confidence interval.

b. Does this sample support HP’s claim?