Combinations of independant normal random variables

Ok a bit stuck with this 1.

Monto sherry is sold in bottles of two sizes - standard and large. For each size, the content, in litres, of a randomly chosen bottle is normally distributed with mean and standard deviation as given in the table

Mean Standard Deviation

Standard Bottle 0.760 0.008
Large Bottle 1.010 0.009

i) I have already worked out that the probability of a randomly chosen standard bottle contains less than 0.750 litres is 0.1056.

ii) Find the probability that a box of 10 randomly chosen standard bottles contains at least 3 bottles whose given contents are each less than 0.750 litres.

Quote:

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Originally Posted by djmccabie

Ok a bit stuck with this 1.

Monto sherry is sold in bottles of two sizes - standard and large. For each size, the content, in litres, of a randomly chosen bottle is normally distributed with mean and standard deviation as given in the table

Mean Standard Deviation

Standard Bottle 0.760 0.008
Large Bottle 1.010 0.009

i) I have already worked out that the probability of a randomly chosen standard bottle contains less than 0.750 litres is 0.1056.

ii) Find the probability that a box of 10 randomly chosen standard bottles contains at least 3 bottles whose given contents are each less than 0.750 litres.

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Let X be the random variable number of standard size bottles whose contents are less than 0.750 litres.

X ~ Binomial(n = 10, p = 0.1056).

Calculate .