Question: 1) Consider two normal independent random variables X and Y with E[X] = 5, E[Y] = 1, E[X 2 ] = 29, E[Y 2 ]

1) Consider two normal independent random variables X and Y with

E[X] = 5, E[Y] = 1, E[X²] = 29, E[Y²] = 5.

Compute the probability

P(3X 2Y + 5).

Hint: a linear combination of independent normal random variables is normal.

2) Small containers to be loaded on a ship have the distribution of weight with mean = 400 lbs and standard deviation = 50 lbs. Independently sampled containers from this population will be loaded on a large ship. What should the cargo load of the ship be to make sure that the probability to hold 10,000 such loaded containers is (4.5) (where is the cumulative distribution function of the standard normal)?

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