# Combinations of independant normal random variables

• Oct 27th 2008, 05:07 AM
djmccabie
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.
• Oct 27th 2008, 05:20 AM
mr fantastic
Quote:

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.

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 $\Pr(X \geq 3) = 1 - \Pr(X \leq 2)$.