The Rockwell hardness of a metal is determined by impressing a hardened point in

Question

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. (a) If a spetimen is acceplable only if its hardness is betweern 64 and 72, what is the probability that a raidornly chosen specimen has an acceptable hardness? (Rournd your answer to four detial places.) -2.6665 (b If the acceptable range o hardness is 68 c 68 + c or what value ore would 95% o all spec mens have acceptable hardness, ound your answer o two decima 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: binomial variable; wha isp?] (Round your answer to four decirmnal places.) the number among the ten specimens with hardness less than 71841s a

Explanation / Answer

a) Mean = 68

SD = 3

z1 = (64 - 68)/3 = -1.33

z2 = 1.33

P = 0.8165

b) 95% means two SD away

So,

c should be 3 *2 = 6

c) 10 * 0.8165 = 8.17

d) z = (71.84 - 68)/3

z = 1.28

P = 0.8997

P(at most 8) = 1 - (9, 10)

P = 1 - (10C9 * 0.8997^9 * 0.1003^1 + 10C10 * 0.8997^10 * 0.1003^0)

P = 1 - 0.7349

P = 0.2651

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.