Kjsdfjyrbasdhviurhasiudhvr = ?

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Answer 1

Answer:

Answer: option A/ eibfjed

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Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie of this type contains at least two chocolate chips to be greater than 0.99. Find the smallest value of the mean that the distribution can take.

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Answer:

$\lambda \geq 6.63835$

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

$f(x)=(e^(-\lambda) \lambda^x)/(x!) , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

$P(X\geq 2)=1-P(X<2)=1-P(X\leq 1)=1-[P(X=0)+P(X=1)]$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=(e^(-\lambda) \lambda^0)/(0!)=e^(-\lambda)$

$P(X=1)=(e^(-\lambda) \lambda^1)/(1!)=\lambda e^(-\lambda)$

And replacing we have this:

$P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^(-\lambda) +\lambda e^(-\lambda)[]$

$P(X\geq 2)=1-e^(-\lambda)(1+\lambda)$

And we want this probability that at least of 99%, so we can set upt the following inequality:

$P(X\geq 2)=1-e^(-\lambda)(1+\lambda)\geq 0.99$

And now we can solve for $\lambda$

$0.01 \geq e^(-\lambda)(1+\lambda)$

Applying natural log on both sides we have:

$ln(0.01) \geq ln(e^(-\lambda)+ln(1+\lambda)$

$ln(0.01) \geq -\lambda+ln(1+\lambda)$

$\lambda-ln(1+\lambda)+ln(0.01) \geq 0$

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

$x_(n+1)=x_n -(f(x_n))/(f'(x_n))$

Where :

$f(x_n)=\lambda -ln(1+\lambda)+ln(0.01)$

$f'(x_n)=1-(1)/(1+\lambda)$

Iterating as shown on the figure attached we find a final solution given by:

$\lambda \geq 6.63835$

Final answer:

The problem pertains to Poisson Distribution in probability theory, focusing on finding the smallest mean (λ) such that the probability of having at least two chocolate chips in a cookie is more than 0.99. This involves solving an inequality using the formula for Poisson Distribution.

Explanation:

This problem pertains to the Poisson Distribution, often used in probability theory. In particular, we're looking at the number of events (in this case, the number of chocolate chips) that occur within a fixed interval. Here, the interval under study is a single cookie. The question requires us to find the smallest value of λ (the mean value of the distribution) such that the probability of getting at least two chocolate chips in a cookie is more than 0.99.

Using the formula for Poisson Distribution, the probability of finding k copies of an event is given by:

P(X=k) = λ^k * exp(-λ) / k!

The condition here is that the probability of finding at least 2 copies is more than 0.99. Therefore, you formally need to solve the inequality:

P(X>=2) = 1 - P(X=0) - P(X=1) > 0.99

Substituting the values of P(X=0) and P(X=1) from our standard formula, you will need to calculate and find the smallest value of λ that satisfies this inequality.

Learn more about Poisson Distribution here:

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Daryl invested $2,200 for 3 years. He received interest of $264. What was the interest rate?

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Answer:

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

As you go higher up on a mountain,the climate ALWAYS becomes _____A.drier
B.hotter
C.colder
D. Wetter

Answers

C, Colder. :) Above a certain level, the atmosphere loses heat to space faster than is can be warmed either directly (by sunlight) or indirectly (from the ground) so it gets colder and colder. Hope this helps :)

D. Colder is your answer

HELP FATS PLEASE
WILL MARK BRAINLEYST
HOW TO STEP BY STEP SOLVE THIS

Answers

Answer:

Step-by-step explanation:

(y+2)'2-5=20

(y+2)'2=15

y·y+4=15

y·y=11

y=11y

y=5.5

"I think of a number, multiply it by itself and then add 6 to the result”

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Answer:

9x9+6 could be possible

Step-by-step explanation:

Hope this is what you were looking for, have a great day (;

Please helpppp!!! it’s timed!!!! thank u for helping!!!!!

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Answer:

ADMC

Step-by-step explanation:

The secant of a circle is a line that cuts the cuts two points of the circumference with one end point external to the circle;

Fro the given diagram, the two lines that cuts the circumference of the circle at two points are AEB and ADMC

Hence the one that contains diameter with point M is line ADMC

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