The computer that controls a bank's automatic teller machine crashes a mean of 0.5 times per day. What is the probability that, in any seven-day week, the computer will crash less than 3 times? Round your answer to four decimal places.

Answers

Answer 1

Answer:

Answer:

0.3216 = 32.16% probability that, in any seven-day week, the computer will crash less 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:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval

Mean of 0.5

7-day week, so $\mu = 7*0.5 = 3.5$

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

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

In which

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 0) = (e^(-3.5)*(3.5)^(0))/((0)!) = 0.0302$

$P(X = 1) = (e^(-3.5)*(3.5)^(1))/((1)!) = 0.1057$

$P(X = 2) = (e^(-3.5)*(3.5)^(2))/((2)!) = 0.1850$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0302 + 0.1057 + 0.1857 = 0.3216$

0.3216 = 32.16% probability that, in any seven-day week, the computer will crash less than 3 times

Answer 2

Answer:

Final answer:

To find the probability that the computer will crash less than 3 times in a seven-day week, we can use the binomial probability formula.

Explanation:

To find the probability that the computer will crash less than 3 times in a seven-day week, we can use the binomial probability formula. The formula for binomial probability is:

$P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)$

Where:

P(X = k) is the probability of exactly k successes
C(n, k) is the combination function for choosing k items from a set of n
p is the probability of success for each individual trial
n is the number of trials

In this case, the mean number of crashes per day is 0.5, which means the probability of a crash in a single day is 0.5. Since we're interested in the probability of less than 3 crashes in a seven-day week, we can calculate P(X < 3) using the binomial probability formula with n = 7, p = 0.5, and k = 0, 1, 2:

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

Using the binomial probability formula, we can calculate:

$P(X = 0) = C(7, 0) * 0.5^0 * (1-0.5)^(^7^-^0)\nP(X = 1) = C(7, 1) * 0.5^1 * (1-0.5)^(^7^-^1)\nP(X = 2) = C(7, 2) * 0.5^2 * (1-0.5)^(^7^-^2)$

Adding these probabilities together will give us the probability of less than 3 crashes in a seven-day week.

Rounding the final probability to four decimal places, we get the probability that the computer will crash less than 3 times in a seven-day week.

Learn more about Binomial probability here:

brainly.com/question/39666605

#SPJ12

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Which function is continuous?

Answers

The answer is D. Cost of U.S. postage as a function of the weight of the letter.

Answer:

The answer is B

Step-by-step explanation:

Did the practice on edge.

What is the reciprocal of 7 1/3? whats the reciprocal?

Answers

The reciprocal of a number in mathematics is referred to as the inverse of that number.

This means that:

Given a number x, its reciprocal is :

$x = x/ 1= 1/x$

Given a number 1/x, its reciprocal is

$1/x = x/1$

The reciprocal of $7(1)/(3)$ is $(3)/(22)$

From the question, $7(1)/(3)$ is called a mixed fraction

Converting to an improper fraction

$7(1)/(3)$ = $(22)/(3)$

The inverse of $(22)/(3)$

$(22)/(3)$ = $(3)/(22)$

Therefore, the reciprocal of $7(1)/(3)$ is $(3)/(22)$

To learn more, visit the link below:

brainly.com/question/18054668

Answer:

3/22

Step-by-step explanation:

Reciprocal means the inverse of the fraction. For your mixed number 7 and 1/3, turn it into fraction by multiplying 7 with the denominator which is 3, then add the numerator which is 1 to get the numerator of a normal fraction which is 22. The numerator remains the same.

The fraction is 22/3. As mentioned above, reciprocal means the inverse, so the final answer is 3/22

Express the following in exponential notation:
(-13) X (-13).
35 times

Answers

Answer:

$(-13) * (-13) = (-13)^(2)$

$35 * 35 = 35^(2)$

Step-by-step explanation:

Given

$(-13) * (-13)$

Required

Express as an exponential notation

$(-13) * (-13)$

Apply the following law of indices

$x^a * x^b = x^(a+b)$

This gives:

$(-13) * (-13) = (-13)^(1+1)$

$(-13) * (-13) = (-13)^(2)$

The second complete is incomplete; However, I'll assume it is: 35 times 35

$35 * 35$

Using the same law applied in (1) above:

$35 * 35 = 35^(1+1)$

$35 * 35 = 35^(2)$

Mr. Hoya brought 5 watermelons from his grocery store. The watermelons weighed 8.25 pounds, 9.25 pounds, 8.875 pounds, 9.625 pounds and 10.75 pounds. At the party, 153 people each ate a 0.25 pound serving of watermelon. Was the amount of leftover watermelon less than, greater than, or equal to 8.5 pounds? Explain how to solve the problem.

Answers

The first thing we must do for this case is to find the total weight of the watermelons.
We have then:
$W = 8.25 + 9.25 + 8.875 + 9.625 + 10.75 W = 46.75 pounds$
We now look for the amount of watermelons that people ate.
We have then:
$(0.25) * (153) = 38.25 pounds$
Therefore, the amount of watermelon remaining is:
$46.75 - 38.25 = 8.5 pounds$
We note that the amount of watermelon remaining is equal to 8.5 pounds.
Answer:
the amount of leftover watermelon is: equal to 8.5 pounds

Answer:
The amount of leftover watermelon is equal to 8.5 pounds

Explanation:
1- getting the total weight of the watermelon:
The total weight of the watermelon will be the summation of the weights of the 5 watermelons he bought.
This means that:
Total weight = 8.25 + 9.25 + 8.875 + 9.625 + 10.75
Total weight = 46.75 pounds

2- getting the weight of the eaten watermelon:
We know that at the party, there were 153 people and each ate 0.25 of a pound of watermelon.
This means that:
amount eaten = 153 * 0.25
amount eaten = 38.25 pounds

3- getting the weight of the leftover:
weight of leftover = total weight - amount eaten
We have:
Total weight = 46.75 pounds
amount eaten = 38.25 pounds
Therefore:
weight of leftover = 46.75 - 38.25
weight of leftover = 8.5 pounds

Hope this helps :)

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