# Thread: Stats help!

1. ## Stats help!

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

2450 grammes.

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

N 2.15, 0.022.

Find the proportion of tubes with an internal diameter less than
2

.19cm.

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

.20cm.

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!

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