Mathematics, 29.10.2020 17:10 jmitial

What is the probability that from a sample of 100 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI

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Answer from: leah1386

Complete Question

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city’s own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 100 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI?

The value is P(X < 0.95) = 0.95224

Step-by-step explanation:

From the question we are told that

The proportion that wants Giants to win p = 0.90

The sample size is n = 100

Generally the mean of this sampling distribution is

$\mu_{x} = 0.90$

Generally the standard deviation is

$\sigma = \sqrt{\frac{p(1- p)}{n} }$

=> $\sigma = \sqrt{\frac{ 0.90 (1- 0.90)}{100} }$

=> $\sigma = 0.03$

Generally the probability that from a sample of 100 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is mathematically represented as

$P(X < 0.95) = P(\frac{ X - \mu_{x}}{\sigma} < \frac{0.95 -0.90}{0.03} )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

P(X < 0.95) = P(Z < 1.667 )

=> P(X < 0.95) = 0.95224

Answer from: Quest

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

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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