Steel rods are manufactured with a mean length of 25.10cm. There is a variabilit

Question

Steel rods are manufactured with a mean length of 25.10cm. There is a variability in the manufacturing process, the lengths of the rods are Normally distributed with a standard deviation of 0.08cm.

A. Rods that are between 25.03cm and 25.20cm in length are suitable for an automotivee gear assembly built by another company. What proportion of rods are suitable?

B. If an order comes in for 12000 rods that are suitable for the gear assembly, how many rods should the plant manager manufacture?

C. The shortest 3% of rods are unusable and must be scrapped. How short are these rods?

Less than______ cm long (Nearest 0.01cm)

Explanation / Answer

Ans:

Given that

mean=25.10

standard deviation=0.08

a)

z(25.03)=(25.03-25.10)/0.08=-0.875

z(25.20)=(25.20-25.10)/0.08=1.25

P(-0.875<z<1.25)=P(z<1.25)-P(z<-0.875)=0.8944-0.1908=0.7036

b)As,70.36% will be suitable,so plant manager should manufacture more number of rods.

n*0.7036=12000

n=12000/0.7036=17056

c)P(Z<=z)=0.03

z=-1.88

x=25.1-1.88*0.08=24.95

it should be less than 24.95

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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