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-Dominant- [34]

2 years ago

11

A student repeatedly measures the mass of an object using a mechanical balance and gets the following values: 560 g, 562 g, 556

g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g Calculate the standard deviation of his measurements

1 answer:

MrRissso [65]2 years ago

6 0

Answer: 2.76 g

Step-by-step explanation:

The formula to find the standard deviation:-

$\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{n}}$

The given data values : 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g.

Then, $\overline{x}=\dfrac{\sum_{i=1}^{10} x_i}{n}\\\\\Rightarrow\ \overline{x}=\dfrac{560+562+556+558+560+556+559+561+565+563}{10}\\\\\Rightarrow\ \overline{x}=\dfrac{5600}{10}=560$

Now, $\sum_{i=1}^{10}(x_i-\overline{x})^2=0^2+2^2+(-4)^2+(-2)^2+0^2+(-4)^2+(-1)^2+1^2+5^2+3^2\\\\\Rightarrow\ \sum_{i=1}^{10}(x_i-\overline{x})^2=76$

Then, $\sigma=\sqrt{\dfrac{76}{10}}=\sqrt{7.6}=2.76$

Hence, the standard deviation of his measurements = 2.76 g

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Together Mary, Jane, and Ruth received $30. Mary received $6, Jane received $9, and Ruth received $15. What percent of the $30 d

Likurg_2 [28]

Hey there! :D

So, we know that Jane received $9 out of the $30.

Divide 9 by 30.

9/30= .3

Turn that into a percentage.

.3= 30%

We can check this by finding the other percentages.

Ruth= 15 15/30= .5 50%

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I hope this helps!
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1 year ago

Read 2 more answers

Find ST if S(-3,10) and T(-2,3)

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Answer:

ST = 7.07 units

Step-by-step explanation:

* Lets explain how to find the length of a segment

- The length of a segment whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ can be founded by the rule of the distance

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

* Lets solve the problem

∵ The line segment is ST

∵ S is (-3 , 10)

∵ T is (-2 , 3)

- Assume that S is $(x_{1},y_{1})$ and T is $(x_{2},y_{2})$

∴ $x_{1}=-3$ and $x_{2}=-2$

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∴ $ST=\sqrt{(-2--3)^{2}+(3-10)^{2}}$

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2 years ago

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Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that th

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Answer:

Step-by-step explanation:

(a)

The bid should be greater than $10,000 to get accepted by the seller. Let bid x be a continuous random variable that is uniformly distributed between

$10,000 and $15,000

The interval of the accepted bidding is $[ {\rm{\$ 10,000 , \$ 15,000}]$ , where b = $15000 and a = $10000.

The interval of the provided bidding is [$10,000,$12,000]. The probability is calculated as,

$\begin{array}{c}\\P\left( {X{\rm{ < 12,000}}} \right){\rm{ = }}1 - P\left( {X > 12000} \right)\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{12000}^{15000}\\\end{array}$

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(b) The interval of the accepted bidding is [$10,000,$15,000], where b = $15,000 and a =$10,000. The interval of the given bidding is [$10,000,$14,000].

$\begin{array}{c}\\P\left( {X{\rm{ < 14,000}}} \right){\rm{ = }}1 - P\left( {X > 14000} \right)\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{14000}^{15000}\\\end{array} P(X14000)$

$=1- \frac{[15000-14000]}{5000}\\\\=1-0.2\\\\=0.8$

(c)

The amount that the customer bid to maximize the probability that the customer is getting the property is calculated as,

The interval of the accepted bidding is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The interval of the given bidding is [$10,000,$15,000].

$\begin{array}{c}\\f\left( {X = {\rm{15,000}}} \right){\rm{ = }}\frac{{{\rm{15000}} - {\rm{10000}}}}{{{\rm{15000}} - {\rm{10000}}}}\\\\{\rm{ = }}\frac{{{\rm{5000}}}}{{{\rm{5000}}}}\\\\{\rm{ = 1}}\\\end{array}$

(d) The amount that the customer bid to maximize the probability that the customer is getting the property is $15,000, set by the seller. Another customer is willing to buy the property at $16,000.The bidding less than $16,000 getting considered as the minimum amount to get the property is $10,000.

The bidding amount less than $16,000 considered by the customers as the minimum amount to get the property is $10,000, and greater than $16,000 will depend on how useful the property is for the customer.

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Step-by-step explanation:

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dedylja [7]

Answer:

There is sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds

Step-by-step explanation:

We shall need to formulate the hypotheses but first we need to understand the claim in context of this question. The claim is that the standard deviation of time all women spend washing their hair in the morning is 15 seconds. In mathematical notation, this claim can be written as follows;

σ = 15

Clearly the claim contains an equality sign and thus it qualifies to be our null hypothesis;

H0: σ = 15

The complement of the above hypothesis will be our alternative hypothesis;

Ha: σ ≠ 15

We are then informed that the initial conclusion of the test fails to reject the null hypothesis. In short this implies that we fail to reject the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds since this claim is our null hypothesis. If we fail to reject a claim in hypothesis testing, this implies that there is sufficient evidence to support the claim. Therefore, there is sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds

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