Question: Please, put the process of the calculation and formula . A Scottish distillery has imported a new machine that is used to fill bottles of

Please, put the process of the calculation and formula.

A Scottish distillery has imported a new machine that is used to fill bottles of whisky.

However, the machine cannot fill exactly the same amount of whisky into every bottle.

After one month, it is observed that the quantity poured into a 1 litre bottle is normally

distributed with a mean of 1.02 litres and a standard deviation of 0.1 litres.

1 What is the probability of a bottle of whisky containing less than 0.95 litres?

2 Suppose the new machine can be adjusted to any mean while leaving the standard deviation unchanged. To what mean should we set the machine so that only 1% of bottles contain less than 1 litre?

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