Mathematics, 14.04.2020 18:11 sandygarcia65

A computer program has a bug that causes it to fail once in every thousand runs, on average. In an effort to find the bug, independent runs of the program will be made until the program has failed five times.
a. What is the mean number of runs required?
b. What is the standard deviation of the number of runs required?

Answers: 3

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Answer from: vaeh41

a) The mean number of runs required is 5000.

b) The standard deviation of the number of runs required is 2235.

Step-by-step explanation:

For each time the program is run, there are only two posssible outcomes. Either it fails, or it does not. The probability of failing on each run is independent of other runs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected number of trials for r sucesses is:

$E = \frac{r}{p}$

The standard deviation is:

$S = \sqrt{\frac{r(1-p)}{p^{2}}}$

A computer program has a bug that causes it to fail once in every thousand runs, on average.

This means that $p = \frac{1}{1000} = 0.001$

In an effort to find the bug, independent runs of the program will be made until the program has failed five times.

This means that r = 5

a. What is the mean number of runs required?

$E = \frac{r}{p} = \frac{5}{0.001} = 5000$

The mean number of runs required is 5000.

b. What is the standard deviation of the number of runs required?

$S = \sqrt{\frac{5*(1-0.001)}{(0.001)^{2}}} = 2235$

The standard deviation of the number of runs required is 2235.

Answer from: Quest

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

Can someone plz me 1 to 37 . i will earn 10 points

Answer from: Quest

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation:

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