Mathematics, 05.04.2020 20:18 brian2913

Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using technology.

a.) P (x=1)

b.) P (x=5)

c.) P (x=3)

d.) P (x=less than equal 3)

e.) P(x=greather than or equal 5)

f.) P(x=less than or equal 4)

Answers: 3

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Answers

Answer from: star296

a) P(X=1) = 0.302526b) P(X=5) = 0.010206c) P(X=3) = 0.18522d) P(X≤3) = 0.92953e) P(X≥5) = 0.010935f) P(X≤4) = 0.989065

Explanation:

Binomial experiments are modeled by the formula:

$P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}$

Where

P(X=x) is the probability of exactly x successes $C(n,x)=\dfrac{n!}{x!\cdot (n-x)!}$ p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.n is the number of trials1 - p is the probability of failthere are only two possible outcomes for each trial: success or fail.

a.) P (x=1)

$P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526$

b.) P (x=5)

$P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206$

c.) P (x=3)

Using the same formula:

P(X=3)=0.18522

d.) P (x less than or equal to 3)

P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)

Also,

P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)

You can use either of those approaches. The result is the same.

Using the second one:

P(X=4) = 0.059335P(X=5) = 0.010206P(X=6) = 0.000729P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953

e.) P(x greather than or equal to 5)

P(X≥5) = P(X=5) + P(X=6)P(X≥5) = 0.010206 + 0.000729 = 0.010935

f.) P(x less than or equal 4)

P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065

Answer from: Quest

idc

step-by-step explanation:

idk

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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Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the fo...

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