Y varies directly with x, and y = 15 when x = 3. What is the value of x when y = 4?

Algebra 2 Standard Deviation

Illusion [34]

Answer:

don't have answer but have how to do them

Step-by-step explanation:

What are z-scores?

A z-score measures exactly how many standard deviations above or below the mean a data point is.

Here's the formula for calculating a z-score:

z=\dfrac{\text{data point}-\text{mean}}{\text{standard deviation}}z=

standard deviation

data point−mean

z, equals, start fraction, start text, d, a, t, a, space, p, o, i, n, t, end text, minus, start text, m, e, a, n, end text, divided by, start text, s, t, a, n, d, a, r, d, space, d, e, v, i, a, t, i, o, n, end text, end fraction

Here's the same formula written with symbols:

z=\dfrac{x-\mu}{\sigma}z=

σ

x−μ

z, equals, start fraction, x, minus, mu, divided by, sigma, end fraction

Here are some important facts about z-scores:

A positive z-score says the data point is above average.

A negative z-score says the data point is below average.

A z-score close to 000 says the data point is close to average.

A data point can be considered unusual if its z-score is above 333 or below -3−3minus, 3. [Really?]

Want to learn more about z-scores? Check out this video.

Example 1

The grades on a history midterm at Almond have a mean of \mu = 85μ=85mu, equals, 85 and a standard deviation of \sigma = 2σ=2sigma, equals, 2.

Michael scored 868686 on the exam.

Find the z-score for Michael's exam grade.

\begin{aligned}z&=\dfrac{\text{his grade}-\text{mean grade}}{\text{standard deviation}}\\ \\ z&=\dfrac{86-85}{2}\\ \\ z&=\dfrac{1}{2}=0.5\end{aligned}

z

=

standard deviation

his grade−mean grade

=

2

86−85

=

2

1

=0.5

Michael's z-score is 0.50.50, point, 5. His grade was half of a standard deviation above the mean.

Example 2

The grades on a geometry midterm at Almond have a mean of \mu = 82μ=82mu, equals, 82 and a standard deviation of \sigma = 4σ=4sigma, equals, 4.

Michael scored 747474 on the exam.

Find the z-score for Michael's exam grade.

\begin{aligned}z&=\dfrac{\text{his grade}-\text{mean grade}}{\text{standard deviation}}\\ \\ z&=\dfrac{74-82}{4}\\ \\ z&=\dfrac{-8}{4}=-2\end{aligned}

z

=

standard deviation

his grade−mean grade

=

4

74−82

=

4

−8

=−2

Michael's z-score is -2−2minus, 2. His grade was two standard deviations below the mean.

https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/z-scores/a/z-scores-review

this should help

6 0

3 years ago

Can i have some help i spent a lot of points and it didn't work :((((

Ivahew [28]

Answers for A:

Factored form: (x-2)(x+4)

Zeros: x = 2, -4

Vertex: (-1, -9)

Answers for B:

Factored form: -(x+2)(x+7)

Zeros: x = -2, -7

Vertex: (-9/2, 25/4)

5 0

2 years ago

Does 27.93 equal to this 20.7+0.9+0.03

nexus9112 [7]

No,27.93 equals <span>20.00+7.00+0.9+0.03</span>

5 0

3 years ago

Find the value of X<br> Need help ASAP

joja [24]

Answer:

lalal idek

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

2. It is well known that astronauts increase their height in space missions because of the lack of gravity. A question is whethe

Rama09 [41]

Answer:

a) $\bar d = \frac{12.6 +14.4 +14.7 +14.5 +15.2 +13.5}{6}=14.15$

b) $ME=2.57 \frac{0.940}{\sqrt{6}}=0.986$

c) $14.15 - 2.57 \frac{0.940}{\sqrt{5}}=13.164$

$14.15 + 2.57 \frac{0.940}{\sqrt{5}}=15.136$

The 95% confidence interval is given by (13.164.15.136)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

Part a

12.6 14.4 14.7 14.5 15.2 13.5.

Assuming that the men in this study are representative of the population of all men, what is an estimate of the population mean increase in height after three full days in bed?

For this case the best estimate for the mean is the average given by this formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

For our case we are taking differences so would be the mean of differences and we got:

$\bar d = \frac{12.6 +14.4 +14.7 +14.5 +15.2 +13.5}{6}=14.15$

Part b

Assuming 95 % of confidence level. In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by: