A pharmaceutical company has a machine to fill the liquid medicine to a bottle l

Question

A pharmaceutical company has a machine to fill the liquid medicine to a bottle labeled as "6 oz medicine". The amount of medicine filled into a bottle is a random variable X. Assume that X ~ N(6.05. 0.06^2). The company has a specification 6.05 plusminus 0.15 oz. Give the LSL and USL; Find the probability that the bottle contains medicine less than LSL; Find the probability that the bottle contains medicine more than USL; Find the probability that a bottle contains the amount of medicine within the specification limits (a conforming bottle); If governments regulate the company that no more than 10% of bottles can contain less than 6 oz medicine (or P(X

Explanation / Answer

a. LSL=6.05-0.15=5.9 and USL=6.2

c. From information given, Xi=6.2, Xbar=6.05, s=0.06. Substitute the values in the following z score formula to get the required probability.

z=(Xi-Xbar)/s=(6.2-6.05)/0.06=2.5

Look at z table to find area corresponding to z=2.5, which is 0.4938 [ans].

b. Xi=5.9, Xbar=6.05, s=0.06

z=(5.9-6.05)/0.06=-2.5. The required probability is area corresponding to the z score, that is 0.0062.[ans]

d. The required probability is obtained by subtracting the smaller area from the larger area corresponding to z scores. 0.4876 (0.4938-0.0062)

e. From information, z=0.10, Xi=6 and s=0.06 . Substitute the values in z score formula to obtain Xbar (or the process mean mu).

0.10=(6-Xbar)/0.06

Xbar=5.994 [ans]

0.10=(6-Xbar)/0.06

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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