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3 years ago

Calculate the variance and the standard deviation of the data below 23. 19, 22, 30, 28

Mathematics

1 answer:

Alina [70]3 years ago

7 0

To get the variance, start with finding the mean of your data points:

(23 + 19 + 22 + 30 + 28) / 5 = 24.4

Now take each data point and subtract the mean from it, then square that value:

23 - 24.4 = -1.4 * -1.4 = 1.96

19 - 24.4 = -5.4 * -5.4 = 29.16

22 - 24.4 = -2.4 * -2.4 = 5.76

30 - 24.4 = 5.6 * 5.6 = 31.36

28 - 24.4 = 3.6 * 3.6 = 12.96

Now get the average of those new numbers. That is your variance:

(1.96 + 29.16 + 5.76 + 31.36 + 12.96) / 5 = 16.24

The standard deviation will be the square root of the variance:

√(16.24) = 4.0299 (rounded to 4DP)

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Find the equation for intercept x 4 and y -7

nadezda [96]

Answer:

y = $\frac{-7x}{4} - 14$

Step-by-step explanation:

The equation used to find the equation for a line with two intercepts is called point slope form. $y - y_{1} = m(x - x_{1})$ , where $y_{1}$ and $x_{1}$ are the intercept points and m is the slope.

However, we need the slope to use this formula.

Use $m = \frac{y_{1} - y_{2} }{x_{1} - x_{2}}$

m = \frac{y_{1} - y_{2} }{x_{1} - x_{2}}

$m = \frac{((0) - (7))}{((4) - (0))}$

$m = \frac{-7}{4}$

$y - y_{1} = m(x - x_{1})$

y - ( -7 ) = m ( x - ( 4 ) )

y - ( -7 ) = -7/4 ( x - ( 4 ) )

y + 7 = -7/4 ( x + 4 )

y + 7 = $\frac{-7(x+4)}{4}$

y + 7 = $\frac{-7x-28}{4}$

y + 7 = $\frac{-7x}{4} - 7$

y + 7 = $\frac{-7x}{4} - 7$ - 7

y = $\frac{-7x}{4} - 14$

8 0

3 years ago

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iris [78.8K]

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3 years ago

A true/false test has 40 questions. Suppose a passing grade is 30 or more correct answers. Test the claim that a student knows m

Angelina_Jolie [31]

Answer:

z≈3.16

p≈0.001

we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.

Step-by-step explanation:

As a result of step 2, we can assume normal distribution for the null hypothesis

z statistic is computed as follows:

z= $\frac{X-M}{\frac{\sqrt{p*(1-p)} }{\sqrt{N} } }$ where

X is the proportion of correct answers in the test ( $\frac{30}{40}$ )
M is the expected proportion of correct answers according to the null hypothesis (0.5)

p is the probability of correct answer (0.5)
N is the total number of questions in the test (40)

z= $\frac{0.75-0.50}{\frac{\sqrt{0.5*(0.5)} }{\sqrt{40} } }$ ≈ 3.16

And corresponding p value for the z-statistic is p≈0.001.

Since p<0.05, we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.

7 0

3 years ago

Annie works as both a carpenter and a blacksmith. Last week she worked 12 hours as a carpenter and 20 hours as a blacksmith and

Minchanka [31]

Answer:Let x = pay per hour as a carpenter and y = pay per hour as a blacksmith

Last week she worked 12 hours as a carpenter

earning 12x dollars

and 20 hours as a blacksmith

earning 20y dollars

and earned a total of $860

and those two things add up to 860.

Do the same with the other sentence, giving you a second equation.

Step-by-step explanation:

6 0

3 years ago

Is .111111111... a rational number? Yes or No?

Mashcka [7]

Answer:

The answer is no this number is not rational.

Step-by-step explanation:

Because, To show that the rational numbers are dense:

It cannot be expressed as a fraction with integer values in the numerator and denominator. When an irrational number is expressed in decimal form, it goes on forever without repeating.

8 0

3 years ago

Read 2 more answers