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Ilya [14]
3 years ago
8

g A sample of 3 items is chosen at random from a box containing 20 items, out of which 4 are defective. Let X be the number of d

efective items in the sample. Find Var (X), σX, Var (20 − X) and σ20−X.
Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

The variance and standard deviation of <em>X</em> are 0.48 and 0.693 respectively.

The variance and standard deviation of (20 - <em>X</em>) are 0.48 and 0.693 respectively.

Step-by-step explanation:

The variable <em>X</em> is defined as, <em>X</em> = number of defective items in the sample.

In a sample of 20 items there are 4 defective items.

The probability of selecting a defective item is:

P (X)=\frac{4}{20}=0.20

A random sample of <em>n</em> = 3 items are selected at random.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 3 and <em>p </em>= 0.20.

The variance of a Binomial distribution is:

V(X)=np(1-p)

Compute the variance of <em>X</em> as follows:

V(X)=np(1-p)=3\times0.20\times(1-0.20)=0.48

Compute the standard deviation (σ (X)) as follows:

\sigma (X)=\sqrt{V(X)}=\sqrt{0.48}=0.693

Thus, the variance and standard deviation of <em>X</em> are 0.48 and 0.693 respectively.

Now compute the variance of (20 - X) as follows:

V(20-X)=V(20)+V(X)-2Cov(20,X)=0+0.48-0=0.48

Compute the standard deviation of (20 - X) as follows:

\sigma (20-X)=\sqrt{V(20-X)} =\sqrt{0.48}0.693

Thus, the variance and standard deviation of (20 - <em>X</em>) are 0.48 and 0.693 respectively.

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Therefore, the possible lengths (in whole inches) for the third side is

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Step-by-step explanation:

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Answer:

a) (0.555, 0) and (6, 0)

b) r = -3 and r = 1.8

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Set each term in the numerator and denominator equal to 0 and find r.

In the numerator:

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In the denominator:

r = 9/5, 7/8, or -3

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Zeros in the denominator that aren't in the numerator are vertical asymptotes.

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m(0) = (5)² (-6)² / ( (9)² (3)² )

m(0) = 1.235

The m(r)-intercept is (0, 1.235).

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