Write an expression that is equivalent to 3(2t+6)-4t.

At least 96.00% of the data in any data set lie within how many standard deviations of the mean? Explain how you arrived at yo

zheka24 [161]

The answer assumes that the question is about the normal distribution.

Answer:

96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the standard normal distribution that permits obtaining any probability from any normally distributed data, doing the following transformation:

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

That is, in this case, we subtract a given value x from the population mean and then divide the result by the population standard deviation. This is a z-score, and this value is associated with the probability for a standard normal distribution, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the standard normal distribution, there is associated a ubiquitous standard normal table for possible values of z and the corresponding probability. Then, knowing that the data are normally distributed and having both distribution parameters, namely, the population mean and population standard deviation, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that the z-score value tells us how many standard deviations from the mean are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a cumulative standard normal table from the mean.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a cumulative standard normal table from the mean. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

Thus, 96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

5 0

3 years ago

What is the quotient of 1.728 x 109 and 4.8 x 106 expressed in scientific notation?

fenix001 [56]

Step-by-step explanation:

$\to 1,728 \times {10}^{9}$

$= 1,728 \times {10}^{9}$

$= 1,728 \times 1.000.000.000$

$= 1.728.000.000$

$1,728 \times {10}^{9} = 1.728.000.000$

$\:$

$\to 4,8 \times {10}^{6}$

$= 4,8 \times {10}^{6}$

$= 4,8 \times 1.000.000$

$= 4.800.000$

$4,8 \times {10}^{6} = 4.800.000$

4 0

2 years ago

A recipe will make 10 pancakes that are 8 inches in diameter. If you decide to

pashok25 [27]

10 pancakes produces 8 inches in diameter.
The area of 1 pancake is
Area = pi * r^2
Area = pi * 4^2
Area = 50.27 in^2
Then multiply it by 10
Total area = 502.65 in^2

A smaller pancake
Area = pi * r^2
Area = pi * 2^2
Area = 12.56 in^2

Divide 502.65 by 12.56
= 502.65 / 12.65
= 39.74

So there are 39 pancakes.

8 0

3 years ago

Simplify (x*3 +3x*2+6) - (9x*2-5x+7)

zloy xaker [14]

\left[x \right] = \left[ \frac{-1}{4}\right][x]=[4−1] = x*3 +3x*2+6) - (9x*2-5x+7

6 0

2 years ago

Read 2 more answers

Write the equation of the line parallel to 3x - 4y = 18 that goes through the point (8,-3)

kkurt [141]

Answer:

y=3/4x-9