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slega [8]
2 years ago
14

A travelling salesman sells milkshake mixing machines and on average sells 8.9 machines per month. He needs to sell at least 3 m

achines each month order to stay in business, otherwise he will shut down. Using the Poisson distribution, what is the probability he will have to shut down after this month
Mathematics
1 answer:
Goshia [24]2 years ago
5 0

Answer:

0.67% probability he will have to shut down after this month

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

On average sells 8.9 machines per month.

So \mu = 8.9

Using the Poisson distribution, what is the probability he will have to shut down after this month

If he sells less than 3 machines.

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

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-8.9}*8.9^{0}}{(0)!} = 0.0001

P(X = 1) = \frac{e^{-8.9}*8.9^{1}}{(1)!} = 0.0012

P(X = 2) = \frac{e^{-8.9}*8.9^{2}}{(2)!} = 0.0054

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0001 + 0.0012 + 0.0054 = 0.0067

0.67% probability he will have to shut down after this month

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abruzzese [7]

Answer:

\theta = 216

Step-by-step explanation:

Given

Area of Sector : Area of Circle = 3 : 5

Required

Determine the central angle

The question implies that

\frac{Area_{sector}}{Area_{circle}} = \frac{3}{5}

Multiply both sides by 5

5 * \frac{Area_{sector}}{Area_{circle}} = \frac{3}{5} * 5

5 * \frac{Area_{sector}}{Area_{circle}} = 3

Multiply both sides by Area{circle}

5 * \frac{Area_{sector}}{Area_{circle}} * Area_{circle} = 3 * Area_{circle}

5 * {Area_{sector} = 3 * Area_{circle}

Substitute the areas of sector and circle with their respective formulas;

Area_{sector} =\frac{\theta}{360} * \pi r^2

Area_{circle} = \pi r^2

So, we have

5 * \frac{\theta}{360} * \pi r^2 = 3 * \pi r^2

Divide both sides by \pi r^2

5 * \frac{\theta}{360} * \frac{ \pi r^2}{\pi r^2} = 3 * \frac{\pi r^2}{\pi r^2}

5 * \frac{\theta}{360} = 3

Multiply both sides by 360

360 * 5 * \frac{\theta}{360} = 3 * 360

5 * \theta = 3 * 360

Divide both sides by 5

\frac{5 * \theta}{5} = \frac{3 * 360}{5}

\theta = \frac{3 * 360}{5}

\theta = \frac{1080}{5}

\theta = 216

Hence, the central angle is 216 degrees

3 0
2 years ago
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Answer:

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Step-by-step explanation:

4 0
2 years ago
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Step-by-step explanation:

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The Slow Fix auto shop charges $28 for parts and $48 per hour of labor. The We Work Cheaper auto shop charges $59 for parts and
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Answer: 10 hours

Step-by-step explanation:

Given

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We work charge $59 for parts and $44.90 per hour of labor

Suppose both works for x hours

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Cost of We work= \$(59+44.90x)

When these costs are the same

28+48x=59+44.90x\\3.1x=31\\x=10\ hours

6 0
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A local phone company charges a monthly fee of $34.99 plus $.05 for each minute of long distance calls. Parts of minutes are rou
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53.24-34.99=18.25

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20x97=1,940 minutes

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maximum=1,940 minutes

Hope this helps.

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