The owner of a popular barber shop in stanbul is anxious about reducing the total time a custommer spends (i.e waiting to be served plus

The owner of a popular barber shop in İstanbul is anxious about reducing the total time a custommer spends (i.e waiting to be served plus time served) in the barber shop. They randomly select four custommers each day and find the total time they spent in the shop. Using these four observations they find the sample mean and range. These observations are repeated for 25 days. The summary data for these 25 samples are given as:

Mean of the 25 sample means = 50 and the mean of 25 sample Ranges = 12.

(a)    Construct the X- and R- chart upper and lower control limits. [18 points]

(b)    Find the percentage of custommers who will not have spent more than 60 minutes in the shop, assuming that time spend in the barber shop is distributed normally. [16 points]

(c)     The owner of the barber shop, reduces the average time spent in shop to 40 minutes by employing more workers. With this new average time what proportion of custommers will have to stay in the shop longer than 50 minutes? [16 points]