The rockwell hardness of a metal is determined by

Reference no: EM13629980

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 68 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.)

(a) If a specimen is acceptable only if its hardness is between 65 and 71, what is the probability that a randomly chosen specimen has an acceptable hardness? (Round your answer to four decimal places.)

(b) If the acceptable range of hardness is (68 ? c, 68 + c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.)

(c) If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places.)
_______ specimens

(d) What is the probability that at most eight of ten independently selected specimens have a hardness of less than 71.84? [Hint: Y = the number among the ten specimens with hardness less than 71.84 is a binomial variable; what is p?] (Round your answer to four decimal places.)

Reference no: EM13629980

Questions Cloud

Air flows steadily through an insulated 5 cm constant : air flows steadily through an insulated 5 cm constant diameter duct fitted with a fan. the air enters the suction side

Calculate the final temperature when 1600g of water at 35oc : calculate the final temperature when 1600g of water at 35oc in a 125g cu calorimeter is mixed with 128g of steam

Assume that a person is on a roof and that the structure : assume that a person is on a roof and that the structure has a circular cross section. if the interface is frictionless

Air in a piston-cylinder assembly undergoes a process from : air in a piston-cylinder assembly undergoes a process from state 1 where t1 300 k p1 100 kpa to state 2 where t2500 k

The rockwell hardness of a metal is determined by : the rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then

Car a is speeding in the positive x direction and is about : car a is speeding in the positive x direction and is about to run through a red light and collide with car b heading

For an unpolarized electric field ie the electric field has : for an unpolarized electric field i.e. the electric field has polarization components both parallel and perpendicular

Calculate the entropy generated in the process in kjk use : a well-insulated chamber is divided in two parts my a thin membrane. the left side with a volume of 2000 cm3 is filled

Suppose iq scores were obtained from randomly selected : suppose iq scores were obtained from randomly selected couples. for 20 such pairs of people the linear correlation

User Account

All Pages