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# Normal Distribution Probability help please watch

1. The mean weight of a bottle is 506 grams.
The standard deviation is 12 grams.
The Stated weight on the bottle is 500 grams.

1) Find the weight such that only 5% of the bottles contain less than the stated weight of 500 grams.

For this question I got an answer of 525.8 grams

2) What value would the mean weight need to be to ensure that only 1% of bottles contain less than the stated weight of 500 grams.

For this question I got 527.96

3) Find the probability that the bottle contains more than 520 grams.

For this question i got 0.123

Can you please tell me if my answers are correct or where I went wrong.
Thank you
2. (Original post by tupac1111)
The mean weight of a bottle is 506 grams.
The standard deviation is 12 grams.
The Stated weight on the bottle is 500 grams.

1) Find the weight such that only 5% of the bottles contain less than the stated weight of 500 grams.

For this question I got an answer of 525.8 grams

2) What value would the mean weight need to be to ensure that only 1% of bottles contain less than the stated weight of 500 grams.

For this question I got 527.96

3) Find the probability that the bottle contains more than 520 grams.

For this question i got 0.123

Can you please tell me if my answers are correct or where I went wrong.
Thank you
I'm only using 3/4 fig. tables, so bear that in mind.

1) Can't make sense of this question. Given the mean weight and stated weight, the percentage weighing less than 500g is fixed. If you mean find the mean weight such that..., then I'd say 519.74 ish. I.e. 500 + 1.645 S.D.

2) I make it 527.91 i.e. 500 + 2.326 S.D.

3) 0.1218

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