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Lynna [10]
3 years ago
10

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the

Poisson distribution. Provide answers to the following to 3 decimal places. What is the probability that exactly two customers arrive in a minute? Find the probability that more than three customers arrive in a two-minute period. What is the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute?
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
4 0

Answer:

a)  P(2)=0.270

b) P(X>3)=0.605

c)  P=0.410

Step-by-step explanation:

We know that customers arrive at a grocery store at an average of 2.1 per minute. We use the  Poisson distribution:

\boxed{P(k)=\frac{\lambda^k \cdot e^{-\lambda}}{k!}}

a)  In this case: \lambda=2.1

P(2)=\frac{2.1^2 \cdot e^{-2.1}}{2}\\\\P(2)=0.270

Therefore, the probability is P(2)=0.270.

b)  In this case: \lambda=2\cdot 2.1=4.2

P(X>3)=1-P(X\leq 3)\\\\P(X>3)=1-\sum_{x=0}^3 \frac{4.2^x \cdot e^{-4.2}}{x!}\\\\P(X>3)=1-0.395\\\\P(X>3)=0.605

Therefore, the probability is P(X>3)=0.605.

c)  We know that two customers came in in the first minute. That is why we calculate the probability of at least 5 customers entering the other 2 minutes.

In this case: \lambda=2\cdot 2.1=4.2

P(X\geq 5)=1-P(X

Therefore, the probability is P=0.410.

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Pavel [41]

Answer:

Step-by-step explanation:

Let j represent the cost of a juice box.

Let w represent the cost of a bottle of water.

One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92.. This means that

18j + 32w = 19.92 - - - - - - - - - - - - 1

The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. This means that

14j + 26w = 15.76- - - - - - - - - - - - 2

Multiplying equation 1 by 14 and equation 2 by 18, it becomes

252j + 448w = 278.88

252j + 468w = 283.68

Subtracting, it becomes

- 20j = - 4.8

j = - 4.8/- 20 = 0.24

Substituting j = 0.24 into equation 1, it becomes

18 × 0.24 + 32w = 19.92

4.32 + 32w = 19.92

32w = 19.92 - 4.32 = 15.6

w = 15.6/32 = 0.4875

Kara's prices are incorrect.

the cost of a juice box is $0.24

the cost of a bottle of water is $0.4875

7 0
3 years ago
Pen are shipped to the office supply store in boxes of 12 each. Write a function rule to calculate the total number of pens when
Tom [10]

p = 12x is the  function rule to calculate the total number of pens when you know the number of boxes

<em><u>Solution:</u></em>

Given that,

Pen are shipped to the office supply store in boxes of 12 each

To find: Write a function rule to calculate the total number of pens when you know the number of boxes

Let "p" be the total number of pens

Let "x" be the number of boxes

Number of pens in each box = 12

Then from given information,

Total number of pens = Number of boxes multiplied by number of pens in each box

p = x \times 12\\\\p = 12x

Thus the function rule is found

6 0
3 years ago
8x6+(12-4)/2 equal what is sum???
algol13
8 \times 6 + \dfrac{(12-4)}{2}

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8 0
3 years ago
Read 2 more answers
4x+5-2=3x+7x-15 I dont get how to get the answer for this please help.
fredd [130]
Hello there! How are you today?

4x + 5 -2 = 3x + 7x - 15

First, we need to get the variable (x) on one side. To do that, we must simplify the right side of the equation, and then decide what to do from there, so let's proceed to do so.

3x + 7x = 10x

4x + 5 - 2= 10x - 15

Now we have x simplified on both sides of the equation. However, we need x to be on one side of the equation in order to solve for it.
Subtract 4x from both sides.

4x - 4x = 0
10x - 4x = 6x

We are now left with:
6x - 15 = 5 - 2

Simplify the right side of the equation.

5 - 2 = 3

6x - 15 = 3

Now we need to isolate x. To isolate x, we need to add 15 to both sides, as x is being subtracted by 15, and adding 15 will cancel it out.

-15 + 15 = 0
3 + 15 = 18

We now are left with:
6x = 18

Now we only have one step left, and that is to solve for x. Since x is being multiplied by 6, we need to perform the opposite order of operations to cancel it out. To do that, we must divide both sides by 6 to solve for x.

6x = 18
Divide both sides by 6.

6x / 6 = x
18 / 6 = 3

We are now left with the solution:

x = 3

I hope this helps!
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Reil [10]
The original price was 4 dollars
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