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djverab [1.8K]
3 years ago
13

What is the value of x

Mathematics
1 answer:
lilavasa [31]3 years ago
4 0

Answer:

x = 1 \\ 159 \times 1 + 1 = 160

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A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distribute
nlexa [21]

Answer:

a. P(x = 0 | λ = 1.2) = 0.301

b. P(x ≥ 8 | λ = 1.2) = 0.000

c. P(x > 5 | λ = 1.2) = 0.002

Step-by-step explanation:

If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

P(k)=\frac{\lambda^{k}e^{-\lambda}}{k!}= \frac{1.2^{k}\cdot e^{-1.2}}{k!}

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

P(0)=\frac{1.2^{0}\cdot e^{-1.2}}{0!}=e^{-1.2}=0.301

b. What is the probability of finding eight or more defective pens in a carton?

This can be calculated as one minus the probablity of having 7 or less defective pens.

P(k\geq8)=1-P(k

P(0)=1.2^{0} \cdot e^{-1.2}/0!=1*0.3012/1=0.301\\\\P(1)=1.2^{1} \cdot e^{-1.2}/1!=1*0.3012/1=0.361\\\\P(2)=1.2^{2} \cdot e^{-1.2}/2!=1*0.3012/2=0.217\\\\P(3)=1.2^{3} \cdot e^{-1.2}/3!=2*0.3012/6=0.087\\\\P(4)=1.2^{4} \cdot e^{-1.2}/4!=2*0.3012/24=0.026\\\\P(5)=1.2^{5} \cdot e^{-1.2}/5!=2*0.3012/120=0.006\\\\P(6)=1.2^{6} \cdot e^{-1.2}/6!=3*0.3012/720=0.001\\\\P(7)=1.2^{7} \cdot e^{-1.2}/7!=4*0.3012/5040=0\\\\

P(k

c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?

We can calculate this as we did the previous question, but for k=5.

P(k>5)=1-P(k\leq5)=1-\sum_{k=0}^5P(k)\\\\P(k>5)=1-(0.301+0.361+0.217+0.087+0.026+0.006)\\\\P(k>5)=1-0.998=0.002

5 0
3 years ago
Which are true?
Tanzania [10]

Answers:

  1. True. All states have a different approach to collecting revenue, which is money they spend on government programs. Most states have income taxes, but a state like Florida doesn't have income taxes. Instead they rely on sales taxes and property taxes. The general rule is that if one tax is missing, then chances are the other tax rates are higher to make up the lack of funds (that the missing taxes would provide).
  2. False. States vary in sales tax rates. For instance, Alabama's sales tax is 4% while Arkansas is 6.5%
  3. True. You can do an online search of "states without sales tax" to find sources to help confirm this. Keep in mind that while the state overall does not impose sales tax, this does not mean the city and/or county governments won't impose sales tax. Unfortunately it's hard to escape taxes and sales tax is just one of those inevitable things.
  4. True. As mentioned in problem 3, local governments (city and/or county) tend to impose taxes of their own on top of state sales taxes. Sales taxes fund state programs while local taxes fund local programs. Though some local government programs will use state or federal dollars.
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Overnight, a pipe cracked and started to leak into a basement. The graph shows the depth of the water in relation to time.
andriy [413]

Answer:

the water will rise 10 in each hour after 4 hours the water will be 40 in deep and it will take 8 hours for the water to reach a depth of 80 in

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3 years ago
Rewrite the expression ”h8”
IceJOKER [234]

Answer:

h x 8

Step-by-step explanation:

when there is no sign in between that means to multiply

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2 years ago
ASAP pls
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1/2

Step-by-step explanation:

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