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liq [111]
3 years ago
13

Each bag of Skittles is supposed to have at least 30 Skittles. A machine that fills bags has a 0.005 probability of under fillin

g a bag. For every thousand bags, what is the standard deviation for the number of bags (out of a thousand) that are under-filled. Assume the Poisson distribution.
Mathematics
1 answer:
telo118 [61]3 years ago
5 0

Answer:

The standard deviation for the number of bags that are underfilled is 2.236.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval. The variance is the same as the mean, which mean that the standard deviation is the square root of the mean.

In this question:

Expected number of underfilled bags in a sample of n bags is:

\mu = 0.005*n

1000 bags, so

\mu = 0.005*1000 = 5

Standard deviation S = \sqrt{5} = 2.236

The standard deviation for the number of bags that are underfilled is 2.236.

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Based on SAS similarity, MPQ and MLN are similar, so their sides are proportional.

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3/16 x 6 in the simplest form
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Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter
mezya [45]

Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

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Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

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We can express the diameter as:

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To optimize we can derive the function and equal to zero.

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