Question

Use the following information for Questions 8, 9, and 10

Soda bottles are filled so that they contain an average of 330 ml of soda in each bottle. Suppose that the amount of soda in a bottle is normally distributed with a standard deviation of 4 ml.

8) What is the probability that a randomly selected bottle will have less than 325 ml of soda?  Round your answer to 4 decimal places.

9) What is the probability that a randomly selected six-pack of soda will have a mean less than 325 ml of soda?  Round your answer to 4 decimal places.

10) What is the probability that a randomly selected twelve-pack of soda will have a mean less than 325 ml of soda?  Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 330

standard deviation = =4

(a) P(x <325 ) = P[(x - ) / < (325 - 330) /4 ]

= P(z <-1.25 )

Using z table,

answer =0.1056

(b ) n = 6

= 330

= / n = 4/ 6 = 1.6330

P( <325 ) = P(( - ) / < (325 - 330) / 1.6330)

= P(z <-3.06 )

Using z table

answer=0.0011

(C) n = 12

= 330

= / n = 4/ 12 = 1.1547

P( <325 ) = P(( - ) / < (325 - 330) / 1.1547)

= P(z <--4.33 )

Using z table

answer = 0