An automatic machine in a manufacturing process is operating properly if the len

Question

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean of 114 cm and a standard deviation of 5.6 cm. A. Find the probability that one selected subcomponent is longer than 116 cm. Probability = Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 116 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 116 cm. Probability =

Explanation / Answer

Mean is 114 and standard deviation is 5.6

A. P(x>116)= P(z>(116-114)/5.6)=1-P(z<0.36). From normal distribution table we get 1-0.6406 =0.3594

B. P(xbar>116)=P(z>(116-114)/(5.6/(sqrt(4))))= P(z>0.71) or 1-P(z<0.71). From normal distribution table we get 1-0.7611 or 0.2389

C. P(all 4 > 116) = [P(one selected > 116) ] = (0.3594)^4 =0.01668

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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