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2 years ago

5

Which expression is equivalent to

n\frac{7\pi }{6}" alt="sin\frac{7\pi }{6}" align="absmiddle" class="latex-formula">?

1 answer:

Ulleksa [173]2 years ago

7 0

Check the picture below.

notice, the pairs in the Unit Circle are the (cosine , sine) pair, which are equivalent to (x , y) values in a cartesian plane.

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A set of normally distributed data has a mean of 3.2 and a standard deviation of 0.7. Find the probability of randomly selecting

jenyasd209 [6]

Answer:

$P(Z> 3.13) = 0.000874$

Step-by-step explanation:

A set of normally distributed data has a mean of 3.2 and a standard deviation of 0.7. Find the probability of randomly selecting 30 values and obtaining an average greater than 3.6.

We can denote the population mean with the symbol $\mu$

According to the information given, the data have a population mean:

$\mu = 3.2$ .

The standard deviation of the data is:

$\sigma = 0.7$ .

Then, from the data, a sample of size $n = 30$ is taken.

We want to obtain the probability that the sample mean is greater than 3.6

If we call

$\mu_m$ to the sample mean then, we seek to find:

$P(\mu_m> 3.6)$

To find this probability we find the Z statistic.

$Z = \frac{\mu_m-\mu}{\sigma_{\mu_m}}$

Where:

Where $\sigma_{\mu_m}$ is the standard deviation of the sample

$\sigma_{\mu_m} = \frac{\sigma}{\sqrt{n}}$

$\sigma_{\mu_m} =\frac{0.7}{\sqrt{30}}\\\\\sigma_{\mu_m} = 0.1278$

$P(\frac{\mu_m-\mu}{\sigma_{\mu_m}}> \frac{3.6-3.2}{0.1278})$

Then:

$Z = \frac{3.6-3.2}{0.1278}\\\\Z = 3.13$

The probability sought is: $P(Z> 3.13)$

When looking in the standard normal probability tables for right tail we obtain:

$P(Z> 3.13) = 0.000874$

8 0

3 years ago

How many 14 inch cubes does it take to fill a box with width 314 inches, length 234 inches, and height 114 inches?

Nesterboy [21]

Answer:

Step-by-step explanation:

First you need to find the area then divide that by 14

3 0

3 years ago

How would you ask a friend "Do you agree?" in Spanish?

Lemur [1.5K]

It's Estas de acuerdo?

8 0

3 years ago

Read 2 more answers

The mean diastolic blood pressure for a random sample of people was millimeters of mercury. If the standard deviation of individ

spin [16.1K]

Answer:

(85.62, 90.38).

Step-by-step explanation:

The missing data can be assumed to be we have the following information:

¯x =88, s=10, n=70

Substituting the values in the following formula, we compute the 95% C.I for true population mean diastolic pressure as shown below:

95% C.I.=¯x±t(0.95,n−1)⋅Sm=¯x±t(0.95,70−1)⋅s√n=88±1.99⋅10√70=(85.62,90.38)

The answer is (85.62, 90.38).

4 0

3 years ago

Find the mean absolute deviation of the following numbers. 10, 8, 5, 12, 20

kicyunya [14]

The mean absolute deviation of the following set of data is 4.5
Step-by-step explanation:
We need to find the mean absolute deviation of the following set of data.
10,20,12,4,18,8,14,18
For finding mean absolute deviation, first we need to find the mean of the given data set.
The formula used to calculate mean is:
Sum of all data points: 10+20+12+4+18+8+14+18 = 104
Number of data points = 8
So, mean is:

Now, we will subtract 13 from the given data points:
10 - 13 = -3
20 - 13 = 7
12 - 13 = -1
4 - 13 = -9
18 -13 = 5
8 - 13 = -5
14 - 13 = 1
18 - 13 = 5
We will take absolute values i.e |-a|=a
So, now the numbers will be:
3,7,1,9,5,5,1,5
We will now find absolute mean deviation by finding mean of newly calculate values
Sum of all data points = 3+7+1+9+5+5+1+5
Number of data points = 8

So, the mean absolute deviation of the following set of data is 4.5

4 0

3 years ago