The data in the accompanying table give the diameter(in thousandths of aninch) of motor shafts that will be used in automobile engines. Each day for 6weekdays, 4 shafts were sampled from the production line and carefully measured. For these shafts to workproperly, the diameter must be about 815 thousandths of an inch. Engineers designed a process that they claim will produce shafts of thisdiameter, with =1 thousandth of an inch. Complete parts a through f.

**Please give step by step** (what is the mean, n, and SD?)

**Please see the dataset attached**

a) If the diameters of shafts produced by this process are normallydistributed, then what is the probability of finding a shaft whose diameter is less than 2 thousandths of an inch below thetarget?

(Round to four decimal places asneeded.)

b) If we measure 95 shaftsindependently, what is the probability that the diameter of every shaft is between 813 and 817 thousandths of aninch? Between 812 and 818thousandths?

The probability that every shaft is between 813 and 817 thousandths of an inch.

(Round to four decimal places asneeded.)

The probability that every shaft is between 812 and 818 thousandths of an inch.

(Round to four decimal places asneeded.)

Full data set Day Week Shaft Diameter Day Week Shaft Diameter 815.4 813.6 815.1 815.4 814.1 815.8 814.6 814.1 815.2 815 813.2 815.2 N N N N - JJJ 4 4 - - - - - - - - - - - - - - W W W W N N N N - - - J 815.4 815.1 817 813.2 815 814.2 814.4 814.3 815.5 816.6 817.2 815.1