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A container ship usually loads 100 containers. The limit of load weight of the ship is...

A container ship usually loads 100 containers. The limit of load weight of the ship is 300 tons. Let X be the weight of a container on the ship measured in tons. For 100 containers to weigh more than 300 tons, the average weight should be greater than 3 tons per container. It is known that the mean and the variance of X are 2.5 and 1, respectively.

Q1. Assume X is normally distributed. What is the probability that a container weighs more than 3 tons?

Q2. We want to calculate the probability that the load exceeds the maximum capacity. Calculate the probability

Q3.  Safety inspection is taken at random times. Since it is impossible to measure the total weight, 25 containers are randomly selected and measured. If the total weight of 25 containers is over 75 tons, the ship fails to pass the inspection. Assume that X is normally distributed. What is the probability that a container ship fails in an inspection?

Math   Statistics-And-Probability   
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