Question

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?

Answer #1

A container ship usually loads 400 containers. The limit of load
weight of the ship is 1300 tons. Let X be the weight of a container
on the ship measured in tons. It is known that the mean and the
variance of X are 3 and 1, respectively.
1. For 400 containers to weigh more than 1,300 tons, the average
weight should be greater than 3.25 tons per container Assume X is
normally distributed. What is the probability that a...

A machine fills containers with a mean weight per container of
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weighs at least 15.8 oz? (c) What is the probability that the
average weight of 9 containers is at least 15.8 oz? (d) What...

The mean weight of loads of rock is 47.0 tons with a standard
deviation of 8.0 tons. If 24 loads are chosen at random for a
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loads is less than 46.5 tons. Assume that the variable is normally
distributed. In addition to the answer, please write out your steps
and thoughts that led you to your answer.

Assume that the weight of marbles are normally distributed with
mean 172 grams and standard deviation 29 grams. a) If 4 marbles are
selected, find the probability that its mean weight is less than
167 grams. b) If 25 marbles are selected, find the probability that
they have a mean weight more than 167 grams. c) If 100 marbles are
selected, find the probability that they have a mean weight between
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Part One
Before every flight, the pilot must verify that the total
weight of the load is less than the maximum allowable load for the
aircraft. The aircraft can carry 42 passengers, and a flight has
fuel and baggage that allows for a total passenger load of 6 comma
7626,762 lb. The pilot sees that the plane is full and all
passengers are men. The aircraft will be overloaded if the mean
weight of the passengers is greater than StartFraction...

1. The weights of a certain brand of candies are normally
distributed with a mean weight of 0.8542 g and a standard deviation
of 0.0521 g. A sample of these candies came from a package
containing 454 candies, and the package label stated that the net
weight is 387.3 g. (If every package has 454 candies, the mean
weight of the candies must exceed 387.3 Over 454= 0.8531
g for the net contents to weigh at least 387.3 g.) a. If...

1). Suppose the weight of a cow is N ( 20000, 400 ). You buy a baby
cow. Find the probability that your baby cow will eventually weigh
20100 pounds or more.
2) How much would you cow have to weigh in order to be bigger than
95% or all cows?
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.25 ). You choose 100 marbles from the box and put them back....

Question 1 Suppose the average height of American adult males is
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of the average height of that sample be? (i.e. the mean of the
sampling distribution) What will the standard deviation of the
average height in that sample be? (i.e. the standard deviation of
the sampling distribution) How big of a sample would we need to...

the following questions are either true or false answers
1. The Central Limit Theorem allows one to use the Normal
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populations.
2. A random sample of 25 observations yields a mean of 106 and
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mean exceeds 110. The probability of exceeding 110 is 0.9525.
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1. The number of hot dogs sold per game at one concession stand
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less than 23,700 hotdogs. Round your answers to four decimal
places.
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