Mathematics, 21.02.2020 05:12 nerdykitty4586

A geological study indicates that an exploratory oil well drilled in a certain region should strike oil with probability 0.1. Assume that striking oil (viewed as success) at one drilling location is independent of success at another location.

(a) Let X be the number of successful strikes if 8 wells are dug. What is the distribution of X.

(b) What is the probability of obtaining at least (inclusive) 3 oil strikes if 8 wells are dug?

(c) If 40 wells are drilled, what is the approximate probability that 8 or fewer will strike oil? Justify your choice of the approximating distribution by verifying the relevant condition(s).

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Answer from: whohelpme

(a) The distribution of X is Binomial distribution.

(b) The probability of obtaining at least 3 oil strikes if 8 wells are dug is 0.0381.

Step-by-step explanation:

Let random variable X = number of exploratory oil well drilled in a certain region should strike oil.

(a)

The probability of successful strike is, P (X) = p = 0.10.

The number of wells dug is, n = 8.

The outcome of the random variable X are:

Successful strike.Unsuccessful strike.

The event of striking oil at one drilling location is independent of success at another location.

The random variables satisfies all the properties of a binomial random variable.

Thus, the distribution of X is Binomial distribution.

(b)

The probability function of a Binomial distribution is:

$P(X=x) ={n\choose x}p^{x}(1-p)^{n-x};\ x=01,2,3,...$

Compute the probability of obtaining at least 3 oil strikes if 8 wells are dug as follows:

P (X ≥ 3) = 1 - P (X < 3)

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

$=1-{8\choose 0}(0.10)^{0}(1-0.10)^{8-0}-{8\choose 1}(0.10)^{1}(1-0.10)^{8-1}\\-{8\choose 2}(0.10)^{2}(1-0.10)^{8-2}\\=1-0.4305-0.3826-0.1488\\=0.0381$

Thus, the probability of obtaining at least 3 oil strikes if 8 wells are dug is 0.0381.

(c)

A Poisson distribution is used to approximate the Binomial distribution when the following conditions are satisfied:

$np\leq 10\\n\geq 20\\P(Success)\ is\ small$

The sample size is, n = 40.

The P (Success) = p = 0.10 (small)

Check the conditions as follows:

$np=40\times0.10=4$

n = 40 > 20.

Thus, a Poisson distribution can be used to approximate the Binomial distribution of the random variable X.

The random variable X thus follows a Poisson distribution with parameter $\lambda=np=4$ .

The probability function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lamda}\lambda^{x}}{x!};\ x=0,1,2,...$

Compute the probability that 8 or fewer wells will strike oil as follows:

P (X ≤ 8) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 8)

$=\frac{e^{-4}(-4)^{0}}{0!}+\frac{e^{-4}(-4)^{1}}{1!}+\frac{e^{-4}(-4)^{2}}{2!}+...+\frac{e^{-4}(-4)^{8}}{8!}\\=0.0183+0.0733+0.1465+...+0.0298\\=0.9786$

Thus, the probability that 8 or fewer wells will strike oil is 0.9876.

Answer from: Quest

it is part of the rising action that reveals public sentiment toward hester.

explanation:

Answer from: Quest

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq and the angle ∠orq are opposite, therefore:

$m\angle opq+m\angle orq=180\°\\\\m\angle opq+ (2x + 16)\°=180\°$

then, $m\angle opq+ (2x + 16)\°=180\°$ can be used to d to calculate the measure of ∠opq

Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to

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A geological study indicates that an exploratory oil well drilled in a certain region should strike...