I have this work could anyone help? I am lost.

A brand of breakfast cereal is available in two sizes: the weights (in

grammes) of the edible contents, and packaging are both Normally distributed

with the following means and standard deviations:

Edible contents Packaging

Small

μ = 465, σ = 10 μ = 25, σ = 3

Standard

μ = 625, σ = 15 μ = 20, σ = 2

.

Find the probabilities that

•

a randomly chosen Standard box has a total weight exceeding 640

grammes,

•

the total weight of the edible contents of 4 randomly chosen Standard

boxes exceeds

the edible contents of 4 randomly chosen Small boxes weigh more

than the edible contents of

3 randomly chosen Standard boxes.

•

the total weight of 4 randomly chosen Small boxes is more than the

total weight of

3 randomly chosen Standard boxes.

•

the total weight of 4 randomly chosen Small boxes is more than the

total weight of

3 randomly chosen Standard boxes when each box also

contains a small toy weighing exactly 50 grammes.

2. A factory makes both rods and copper tubes, with diameters expressed in

centimetres. Due to variations in the manufacturing process, it is known

that the internal diameter of a copper tube is

N 2.2, 0.032, while the

diameter of a rod is

Find the proportion of tubes with an internal diameter less than

2

Find the proportion of rods with a diameter greater than 2.17cm

•

Find the proportion of rods with a diameter between 2.17cm and

2

A rod and tube are chosen at random. Find the probability that the

rod will not pass through the tube.

3. A population consists of the following five values:

24, 26, 29, 30 and 31;

consider sampling

without replacement from this population.

•

List all samples of size three, and compute the mean of each sample.

•

Compute the mean of the distribution of sample means, and the

population mean, and compare these two values.

•

Compare and comment on the spread in the population with that in

the sample means.

Thanks alot!