Question

For problems 17 and 18, assume that cans of coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.12 oz. (17) Find the probability that a single can of coke has at least 12.06 oz. Express your answer as a decimal rounded to four decimal places. (SHOW WORK) FINAL ANSWER:

(18) Find the probability that a case of 36 cans have a mean of at least 12.06 oz. Express your answer as a decimal rounded to four decimal places. HINT: think of a sampling distribution for samples of 36 and first find the standard error, which is the standard deviation of a sampling distribution.

Answer 1

Solution :

Given ,

mean = = 12

standard deviation = = 0.12

P(x >12.06 ) = 1 - P(x<12.06 )

= 1 - P[(x -) / < (12.06-12) / 0.12]

= 1 - P(z <0.5 )

Using z table

= 1 - 0.6915

= 0.3085

probability= 0.3085

(18)

n = 36

= 12

= / n = 0.12/ 36= 0.02

P( > 12.06) = 1 - P( <12.06 )

= 1 - P[( - ) / < (12.06-12) /0.02 ]

= 1 - P(z < 3)

Using z table

= 1 - 0.9987

probability= 0.0013