t is, s3 Suppose the amount of sun block lotion in plas- c bottles leaving a fil

Question

t is, s3 Suppose the amount of sun block lotion in plas- c bottles leaving a filling machine has a normal distribution. The bottles are labeled 300 milliters (ml) but the actual mean is 302 ml and the standard deviation is 2 ml. (a) What is the probability that an individual bottle u by contains less than 299 ml? (b) Tvo bottles can be purchesed together inat n- pack. What is the probability that the mean content of botles in a twin-pack is less than 299 ml? Assume the contents of the two botles water are independent. (e) If you purchase two twin-packs of the lotion what is the probability that only one of the twin-packs has a mean bottle content less than d in a 299 ml?

Explanation / Answer

Ans:

Given that

mean=302

standard deviation=2

a)

z=(299-302)/2=-1.5

P(x<299)=P(z<-1.5)=0.0668

b)

standard error of mean=2/sqrt(2)=1.414

z=(299-302)/1.414=-2.12

P(z<-2.12)=0.0170

c)Let y be the number of twin packs having mean content less than 299.

Then y has binomial distribution with n=2,p=0.017

P(y=1)=2C1*0.0171*(1-0.017)1

=0.0334

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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