Mathematics, 05.05.2020 19:31 josueur9656

A recent survey by the New Statesman on British social attitudes asked respondents if they believe that inequality is too large. The survey found that 74% of the respondents do believe inequality is too large. In a sample of six British citizens, what is the probability that two believe inequality is too large? In a sample of six British citizens, what is the probability that at least two respondents believe that inequality is too large? In a sample of four British citizens, what is the probability that none believe inequality is too large?

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Answer from: aliviadushane

(a) The probability that in a a sample of six British citizens two believe inequality is too large is 0.0375.

(b) The probability that in a a sample of six British citizens at least two believe inequality is too large is 0.9944.

Step-by-step explanation:

The random variable X can be defined as the number of British citizens who believe that inequality is too large.

The proportion of respondents who believe that inequality is too large is, p = 0.74.

Thus, the random variable X follows a Binomial distribution with parameters n and p = 0.74.

The probability mass function of X is:

$P(X=x)={n\choose x}\ 0.74^{x}(1-0.74)^{n-x};\ x=0,1,2,3...n$

(a)

Compute the probability that in a a sample of six British citizens two believe inequality is too large as follows:

$P(X=2)={6\choose 2}\ 0.74^{2}(1-0.74)^{6-2}\\=15\times 0.5476\times 0.00456976\\=0.03753600864\\\approx 0.0375$

Thus, the probability that in a a sample of six British citizens two believe inequality is too large is 0.0375.

(b)

Compute the probability that in a a sample of six British citizens at least two believe inequality is too large as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-[{6\choose 0}\ 0.74^{0}(1-0.74)^{6-0}]-[{6\choose 1}\ 0.74^{1}(1-0.74)^{6-1}]\\\\=1-[1\times 1\times 0.000308915776]-[6\times 0.74\times 0.0011881376]\\\\=1-0.00031-0.0053\\\\=0.99439\\\\\approx 0.9944$

Thus, the probability that in a a sample of six British citizens at least two believe inequality is too large is 0.9944.

(c)

Compute the probability that in a a sample of four British citizens none believe inequality is too large as follows:

$P(X=0)={4\choose 0}\ 0.74^{0}(1-0.74)^{4-0}\\=1\times 1\times 0.00456976\\=0.00456976\\\approx 0.0046$

Thus, the probability that in a a sample of four British citizens none believe inequality is too large is 0.0046.

Answer from: Quest

They sought new allies to germany tried to get mexico to join and put pressure on the us. the us joined the allies because of the lucitania

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

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