Question

(30 pts) The length of a special part manufactured by a GM supplier is uniformly distributed between 380 mm to 390 mm. What is the mean and standard deviation of the length of this part? What is the probability that the length of a randomly selected part is within 1 standard deviation of its mean value? b.

Answer 1

Ans:

Given that

Uniform distribution with a=380 and b=390

a)mean=(a+b)/2=(380+390)/2=385

variance=(b-a)^2/12=(390-380)^2/12=100/12=8.333

standard deviation=sqrt(8.333)=2.89

b)

F(x)=(x-a)/(b-a)=(x-380)/10

Probability that length is within one standard deviation of the mean=2*2.89/10=0.578