Which answer choice shows 38.412 rounded to the nearest half?

A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

2 years ago

Which statements about the graph of the function f(x) = 2x^2– x – 6 are true? Select two options.

Alekssandra [29.7K]

Answer:

Step-by-step explanation:

Please, share the answer options next time.

1) f(x) = 2x^2– x – 6 is a quadratic function.

2) The coefficients of this polynomial are a = 2, b = -1 and c = -6

2) Its graph opens up.

3) The x-value of the axis of symmetry and the vertex is x = -b / (2a), which here comes out to x = -(-1) / [2(2)], or x = 1/4

4) the y coordinate of the vertex is f(1/4), or -6 1/8

5) The vertex is at (1/4, -6 1/8)

6) The y-intercept is at f(0): 2(0)^2 - 0 - 6 = -6 => (0, -6)

3 0

2 years ago

Read 2 more answers

A ----------------------- chart would best describe the steps in the processing of a product.

BlackZzzverrR [31]

A: a flow chart would best describe the steps

4 0

2 years ago

Read 2 more answers

A researcher gathers data on the length of essays (number of lines) and the SAT scores received for a sample of students enrol

LenaWriter [7]

Answer:

(C) The slope of the regression equation is not significantly different from zero

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other wouds we want to check is our slope is significant.

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

(C) The slope of the regression equation is not significantly different from zero

6 0

2 years ago

LESSON 1 SESSION 1

denpristay [2]

Answer:

Between which two tens does it fall? Between 25 and 26 tens

Between which two hundreds does it fall? Between 2 and 3 hundreds

Explanation:

The place-value chart is:

Hundreds Tens Ones

2 5 3

a) Between which two tens does it fall?

Using the place values you can write 253 = 25 × 10 + 3, i.e. 25 tens and 3 ones.

From that you can write:

250 < 253 < 260

250 = 25 × 10 = 25 tens

260 = 26 × 10 = 26 tens

Then, you conclude that 253 is between 25 and 26 tens.

b) Between which two hundreds does it fall?

Using the same reasoning:

253 = 2 × 100 + 5 × 10 + 3 = 253

200 < 253 < 300

200 = 2 hundreds

300 = 3 hundreds

Conclusion: 253 is between 2 hundreds and 3 hundreds.

3 0

2 years ago