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3 years ago

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Choose the family of distributions that best fits the described situation: You want to model the number of lines of code run unt

il the first 'bug' is detected. The probability a line of code has a bug is 0.003 or 0.3%.

1 answer:

damaskus [11]3 years ago

3 0

Answer is : Geometric distribution

Let X be the number of lines of codes run until the first bug is detected

That is X is the random variable which is the number of trials needed to get first success. Success here is detection of bug . Success has constant probability in each trail which is p= 0.003 . That is before the first success we have X-1 failures with probability (1-0.003)

The probability mass function of X is

P(X=x) = (1-p)x-1 p

P(X=x ) = (1-0.003)x-1 *0.003 , x= 1,2,....

This distribution is also Negative Binomial distribution

As geometric distribution is special case of Negative Binomial Distribution

In Negative Binomial distribution , we have r success ( r\geq 1) and the random variable is the number of Bernouli trials needed to get r successes .

If we put , r= 1, that is number of success is 1

Then the given situation , that is number of lines code run(X) before the first bug follow negative binomial distribution

The probability mass function of Negative Binomial distribution is

P(X=x) = (1-p)x-r pr ,x= r , r+1 , .....

The probability mass function of X is

P(X=x, r=1 ) = (1-0.003)x-1 *0.003 , x= 1,2,....

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Quadrilateral ABCD has vertices at A(-3, 3), B(0, 4), C(3, 3),and D(0,2). What word below best describes this quadrilateral?

BaLLatris [955]

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Answer:

D) Rhombus

Step-by-step explanation:

The figure is a parallelogram with equal-length sides, so is a rhombus.

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2 years ago

What is the value of s in the equation 3r = 10 + 5s, when r = 10?

kupik [55]

S = 4

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3 years ago

Read 2 more answers

Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay

castortr0y [4]

Let P = how much each person paid.

P = [(36.96)(0.20) + 36.96]/4

Solve for P to find your answer.

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3 years ago

Consider the computer output below. Fill in the missing information. Round your answers to two decimal places (e.g. 98.76). Test

slamgirl [31]

Answer:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

The 95% confidence interval would be given by (96.625;100.915)

a) $df=n-1= 19-1= 18$

b) $p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

c) The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

$\bar X=98.77$ represent the sample mean

$s=4.77$ represent the sample standard deviation

n=19 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if we have significant difference on the mean of 100, the system of hypothesis would be:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we can calculate the Standard error for the mean like this:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$98.77-1.96\frac{4.77}{\sqrt{19}}=96.625$

$98.77+1.96\frac{4.77}{\sqrt{19}}=100.915$

So on this case the 95% confidence interval would be given by (96.625;100.915)

Part a

The degree of freedom are given by:

$df=n-1= 19-1= 18$

Part b

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

Then since is a two sided test the p value would be:

$p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Part c

If the system of hypothesis on this case are:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu > 100$

The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

7 0

3 years ago

How do you simplify 11 to the power of 6

Misha Larkins [42]

Answer:

1771561

Step-by-step explanation:

You are referring to

$11 {}^{6}$

a formula called Power of Power

$(11 {}^{2} ) {}^{3} = 121 \times 121 \times 121 = 1771561$

8 0

2 years ago