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Travka [436]
3 years ago
6

The computer that controls a bank's automatic teller machine crashes a mean of 0.60.6 times per day. What is the probability tha

t, in any seven-day week, the computer will crash more than 33 times? Round your answer to four decimal places.
Mathematics
1 answer:
OLEGan [10]3 years ago
3 0

Answer:

0.6045 = 60.45% probability that, in any seven-day week, the computer will crash more than 3 times.

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.

The computer that controls a bank's automatic teller machine crashes a mean of 0.6 per day.

7 day week, so \mu = 7*0.6 = 4.2

What is the probability that, in any seven-day week, the computer will crash more than 3 times?

Either it crashes 3 or less times, or it crashes more than 3 times. The sum of the probabilities of these events is decimal 1. So

P(X \leq 3) + P(X > 3) = 1

We want P(X > 3). So

P(X > 3) = 1 - P(X \leq 3)

In which

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = \frac{e^{-4.2}*(4.2)^{0}}{(0)!} = 0.0150

P(X = 1) = \frac{e^{-4.2}*(4.2)^{1}}{(1)!} = 0.0630

P(X = 2) = \frac{e^{-4.2}*(4.2)^{2}}{(2)!} = 0.1323

P(X = 3) = \frac{e^{-4.2}*(4.2)^{3}}{(3)!} = 0.1852

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0150 + 0.0630 + 0.1323 + 0.1852 = 0.3955

P(X > 3) = 1 - P(X \leq 3) = 1 - 0.3955 = 0.6045

0.6045 = 60.45% probability that, in any seven-day week, the computer will crash more than 3 times.

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MrRa [10]

Answer: a)

20 shirts | 349 + 20(4.8)

40 shirts | 349 + 40(4.8)

60 shirts | 349 + 60(4.8)

b) Tn = 349 + n(4.8)

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7 0
2 years ago
Which ordered pairs are solutions to the inequality 3x-4y>5
Sloan [31]

Note: you did not provide the answer options, so I am, in general, solving this query to solve your concept, which anyways would clear your concept.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the inequality

3x-4y>5

All we need is to find any random value of 'x' and then solve the inequality.

For example, putting x=3

3\left(3\right)-4y>5

9-4y>5

-4y>-4

\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}

\left(-4y\right)\left(-1\right)

4y

\mathrm{Divide\:both\:sides\:by\:}4

\frac{4y}{4}

y

So, at x = 3, the calculation shows that the value of y must be less

than 1 i.e. y<1 in order to be the solution.

Let us take the random y value that is less than 1.

As y=0.9 < 1

so putting y=0.9 in the inequality

3\left(3\right)-4\left(0.9\right)

=9-3.6

=5.4

  • As 5.4 > 5

Means at x=3, and y=0.9, the inequality is satisfied.

Thus, (3, 0.9) is one of the many ordered pairs solutions to the inequality 3x-4y>5.

6 0
3 years ago
7. Which dimensions result in the minimum perimeter for a rectangle with area 42.0 cm2?
natali 33 [55]

9514 1404 393

Answer:

  7. d. l = 6.48 cm, w = 6.48 cm

  8. d. square

Step-by-step explanation:

For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.

__

7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.

__

8. In light of the above, the shape is a square.

_____

The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.

8 0
3 years ago
Math lottssssss offf points
yan [13]
Constant of Proportionality = d/t = 90/2 = 45 mph

In short, Constant of Proportionality would be: 45 miles per hour.

Here, d/t = 45
d = 45t

In short, Your Equation would be: d= 45t

Hope this helps!


5 0
3 years ago
Which of the following numbers is not divisible by 4?
vfiekz [6]
106, it can be divided but it is not an even number. it has a decimal. the answer to 106/4 is 26.5:) hope this helped1
3 0
3 years ago
Read 2 more answers
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