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Dmitrij [34]
2 years ago
15

Please help I only have an hour. ​

Mathematics
1 answer:
Goshia [24]2 years ago
4 0

Answer:

Slope (m) = \frac{y}{x} = \frac{2}{3} = 0.66666666666667

Step-by-step explanation:

0 = arctan (\frac{y}{x}) = 33.69006752598°

X = 4 – 1 = 3

Y = 4 – 2 = 2

Distance (d) = \sqrt{x^2+y^2}= \sqrt{13} =3.605551275464

Equation of the line:

y = 0.66666666666667x + 1.3333333333333

or

y=\frac{2}{3}x+\frac{4}{3}

When x=0, y = 1.3333333333333

When y=0, x = -2

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USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eight people at random off
Law Incorporation [45]

Answer:

a) Figure and code attached

b) E(X)=\mu = np = 8*0.2= 1.6

Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28

Sd(X)=\sigma= \sqrt{1.28}= 1.131

c) P(X\geq 7) =0.97

And we can calculate this with the complement rule.

P(X \geq 7) = 1-P(X

So then we have:

P(X \leq 6) = 0.03

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=8, p=0.2)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

We can use the following R code to generate the histogram for this case:

> x <- seq(0,8,by = 1)

> y <- dbinom(x,8,0.2)

> plot(x,y,type = "h",main="Histogram")

And as we can see we got the result on the figure attached. And the distribution seems to be skewed to the right.

Part b

For this case the expected value is given by:

E(X)=\mu = np = 8*0.2= 1.6

The variance is given by:

Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28

And the standard deviation would be:

Sd(X)=\sigma= \sqrt{1.28}= 1.131

Part c

For this case we have the following inequality:

P(X\geq 7) =0.97

And we can calculate this with the complement rule.

P(X \geq 7) = 1-P(X

So then we have:

P(X \leq 6) = 0.03

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

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