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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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