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.

Answers

Answer 1
Answer:

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

Answer 2
Answer:

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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Can answer this
1/2 + 2/5=​

Answers

Answer:

9/10 or 0.9

Step-by-step explanation:

1/2 + 2/5 =

1 × 5 + 2 × 2/2 × 5

5 + 4 = 10

9/10 or 0.9

InFraction=9/10

InDecimal=0.9

Thus,The answer is 9/10 or 0.9

-TheUnknownScientist

Answer:

9/10 or 0.9.

Step-by-step explanation:

1/2 + 2/5 =

5/10 + 4/10 =

5 + 4/10 =

9/10

Melissa put her cat, Herman, on a diet and kept track of his weight. At the end of 4 weeks, she recorded Herman's weight change as −4 1/2 ounces. She noticed that he had lost the same amount of weight each week. What is Herman's weight change each week of the diet? Enter your answer in the box.

Answers

Answer: -1 1/8

Step-by-step explanation: When you have a problem like this, you have to divide.

So you turn the improper fraction into a mixed number which (4 1/2 turns into 9/2) and then you do KCF (Keep Change Flip). So you keep the 9/8, change division into multiplication, and since we are going to put the four over a 1 like this 4/1, we need to change it into 1/4. Then you multiply across. 9x1=9 and 2x4=8 so it would be 9/8. But it's an improper fraction right? So you do long division, and you get -1 1/8.

-103  

if he lost the same weight each week that means -412 (the weight he lost) ÷ 4 (number of weeks) = -103 (amount of weight lost in one week)

Seven more than twice a number is 23.

Answers

Answer:

x=8

Step-by-step explanation:

In other words, you are looking for a number (x) that if you multiply it by two (same as twice) and then add 7, you get 23.

To solve this, you first write the problem as an algebra equation as follows: 2x + 7 = 23

Then you solve the equation by subtracting 7 from both sides, and then divide both sides by 2. Here is the math to illustrate better:

2x + 7 = 23

2x + 7 - 7 = 23 - 7

2x = 16

2x/2 = 16/2

x = 8

Answer:

i think it is 16

Step-by-step explanation:

16 + 7 = 23

Graph or explain how to graph the equation: y = 3x -5

Answers

The graph of the Equation y= 3x- 5 with coordinates (0, 5) and (1.667, 0) is attached below.

We have,

y= 3x - 5

Now, to find the coordinates to plot one the graph put the distinct value of x as

For x= 0

y= -5

then, for x= 1

y= 3 - 5

y= -2

then, for x= 2

y= 6-5

y= 1

and, for x= 3

y= 9 - 5

y= 4

Learn more about Graph here:

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slope intercept form is

y=mx+b

where m is the slope and b is the y intercept

the equation is given in slope intercept form so that the

slope = 3

y-intercept = -5

to graph this you will first place a point on (-5,0) since it's the y intercept.

then since the slope is rise/run and we have 3 (or 3/1) you will start at (-5,0), and from there go up 3 units and to the right one unit. where you end up will be your second point.

hope this helps

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Answers

Really, now, do you think it fair (or realistic) to hope that someone will do all your homework for you?  Please be thoughtful and courteous and post no more than one or two questions at a time.

Rodney Ranger is a shoe salesman for More Co. He is paid $4.60 per hour plus a commission of 3% on all sales. For the week, assuming Rodney works 30 hours and has sales of $2,400, what is his gross pay?

Gross Pay = ($4.60/hr)(30 hrs) + 0.03($2400).  Complete the multiplications to obtain your final answer.


What is the average of the data in the line plot

Answers

Hey there!

The “average” is your “total” or your “mean” of a data set. To find out the average you have to ADD the total numbers in your data & DIVIDE it by the amount of numbers you have in your data.

EXAMPLE:

SET:

10, 20, 30, 40, 50, 60

EQUATION: 10 + 20 + 30 + 40 + 50 + 60 / 6

10 + 20 + 30 + 40 + 50 + 60 / 6

= 30 + 30 + 40 + 50 + 60 / 6

= 60 + 40 + 50 + 60 / 6

= 100 + 50 + 60 / 6

= 150 + 60 / 6

= 210 / 6

= 35

Thus, the mean is: 35

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The average can be found by adding each of the pieces of data on the plot and then dividing it by how ever many pieces of data there are

ie=
 100+300+800=1200
1200/3=400