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3 years ago

Compute the standard deviation for the set of data.

Mathematics

2 answers:

Arisa [49]3 years ago

6 0

Answer:

a. 2.83

Step-by-step explanation:

The standard deviation is the square root of the variance. That is, the square root of the mean of the squares of the deviation scores.

Hence, to calculate the standard deviation, we need to know the mean of the data set.

$mean=\frac{2+4+6+8+10}{5}=\frac{30}{5}=6$

stdev = standard deviation

$stdev=\sqrt{\frac{2^{2}+4^{2}+6^{2}+8^{2}+10^{2} }{5}-mean^{2}}=\sqrt{\frac{4+16+36+64+100 }{5}-6^{2}}=\sqrt{\frac{220 }{5}-36}=\sqrt{44-36}=\sqrt{8}=2.83$

Hope this hepls!

muminat3 years ago

5 0

Answer:

σ =2√2 .....

Step-by-step explanation:

Lets find the mean first

mean = 2+4+6+8+10/5

m = 30/5

m = 6

σ =√1/5[(2-6)²+(4-6)²+(6-6)²+(8-6)²+(10-6)²]

σ = √1/5[(-4)²+(-2)²+(0)²+(2)²+(4)²]

σ=√1/5[(16+4+0+4+16)]

σ = √1/5(40)

σ = √8

Take the square root of 8.

σ =2√2 .....

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Find the perimeter of rhombus star

Degger [83]

Answer:

$4\sqrt{10}$

Step-by-step explanation:

Perimeter of the rhombus, STAR, is the sum of the length of all it's 4 sides.

The coordinates of its vertices are given as,

S(-1, 2)

T(2, 3)

A(3, 0)

R(0, -1)

Length of each side can be calculated using the distance formula given as $d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}$

Find the length of each side ST, TA, AR, RS, using the above formula by plugging in the coordinate values (x, y) of each vertices.

$ST = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

S(-1, 2) => (x1, y1)

T(2, 3) => (x2, y2)

$ST = \sqrt{(2 -(-1))^2 + (3 - 2)^2}$

$ST = \sqrt{(3)^2 + (1)^2} = \sqrt{9 + 1} = \sqrt{10}$

$TA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

T(2, 3) => (x1, y1)

A(3, 0) => (x2, y2)

$TA = \sqrt{(3 - 2)^2 + (0 - 3)^2}$

$TA = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}$

$AR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

A(3, 0) => (x1, y1)

R(0, -1) => (x2, y2)

$AR = \sqrt{(0 - 3)^2 + (-1 - 0)^2}$

$AR = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$

$RS = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

R(0, -1) => (x1, y1)

S(-1, 2) => (x2, y2)

$RS = \sqrt{(-1 - 0)^2 + (2 -(-1))^2}$

$RS = \sqrt{(-1)^2 + (3)^2} = \sqrt{1 + 9} = \sqrt{10}$

$Perimeter = ST + TA + AR + RS$

$Perimeter = \sqrt{10} + \sqrt{10} + \sqrt{10} + \sqrt{10} = 4\sqrt{10}$

4 0

4 years ago

In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more

pogonyaev

Answer:

0.6915

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 88, \sigma = 4[/ex]What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG?This is 1 subtracted by the pvalue of Z when X = 86. So[tex]Z = \frac{X - \mu}{\sigma}$