Find the zeros for function x^4-4x

The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth g

Bingel [31]

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

Step-by-step explanation:

This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 $\\ n \geq 30$ . Mathematically

$\\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean $\\ \mu = 0$ and a population standard deviation $\\ \sigma = 1$ .

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

From the question, we know that

The population mean is $\\ \mu = 88$ WPM
The population standard deviation is $\\ \sigma = 14$ WPM

We also know the size of the sample for this case: $\\ n = 137$ sixth graders.

We need to estimate the probability that a sample mean being greater than $\\ \overline{X} = 89.87$ WPM in the distribution of sample means. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}$

$\\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}$

$\\ Z = 1.5634 \approx 1.56$

This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that $\\ P(\overline{X} < 89.87)$ . Then

$\\ P(z$

However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore

$\\ P(z>1.56) = 1 - P(z$

$\\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594$

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

5 0

3 years ago

Draw a line having a slope of 1/3 and y-intercept of -1

Lilit [14]

Equation for slope=1/3 and y-intercept=-1 is:
y = mx + b
where m is slope and b is y-intercept.
So, equation becomes
y = -1x + 1/3
Now put different values of x in the equation to get corresponding value of y.
x     y
0    1/3
1 -2/3
2 -5/3
3 -8/3
-1    4/3
-2    7/3
-3    10/3

8 0

3 years ago

A rectangular prism has a volume of 729ft^3. The length width and height are the same. What is the length of each side

viktelen [127]

Answer:

9 feet

Step-by-step explanation:

If each side is the equivalent, each side of the prism is the cube root of 729

Cube root of 729 is 9

Each side is 9 feet long

3 0

3 years ago

True or False. All segments have a perpendicular bisector.

puteri [66]

Without drawing a line on a piece of graph paper. If you know the endpoints of the line segment you can determine the equation of the line and the midpoint of the line. The slope of a perpendicular to a line is the negative reciprocal of the slope of the original line. You can then determine the equation of the perpendicular bisector using the point-slope method. Using a compass and straight edge, you can draw the line. set the compass at the endpoint and wide enough to extend beyond the midpoint. Scribe an arc. Without changing the compass use the other end and scribe another arc so that the two arcs intersect. Connect the two points where the arcs intersect and scribe a line through them. That is the perpendicular bisector.

i found this online ^ hope i helped ^-^

8 0

3 years ago

Read 2 more answers

Find the equation of the linear function h that has h(12)=-7 and that is perpendicular to q(a)=1/2a+38.. I don’t understand how

Effectus [21]

Step-by-step explanation:

q(a) = ½a + 38

The slope of q is ½. So the perpendicular slope is -1/½ = -2.

Write h(x) in point-slope form:

h − (-7) = -2 (x − 12)

h + 7 = -2 (x − 12)

Simplify to get slope-intercept form.

h + 7 = -2x + 24

h = -2x + 17

7 0

3 years ago