(I am at a loss at how to do this problem, the correct answers are posted below

Question

(I am at a loss at how to do this problem, the correct answers are posted below but I have no idea how they got those answers, any help would be greatly appreciative! Thank you!)

Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 oz and standard deviation 0.2 oz.

(a) What is the probability that a randomly selected bottle contains a volume less than 12 oz?

(b) What is the probability that the mean volume of a random sample of 49 bottles is less than 12 oz?

Answer 1:

Correct Answer

0.3085

You Answered

0.4800

Answer 2:

Correct Answer

0.0002

You Answered

0.3632

Explanation / Answer

these answer are from normal distribution can you tell me which disttribution you were applying so that I may help

1)

here probability that a randomly selected bottle contains a volume less than 12 oz =P(X<12) =P(Z<(12-12.1)/0.2)

=P(Z<-0.5)=0.3085

2) for n=49 ; std error of mean =std deviaiton/(n)1/2 =0.2/(49)1/2 =0.02857

hence P(Xbar<12) =P(Z<(12.0-12.1)/0.02857)=P(Z<-3.5)=0.0002

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