Mathematics: Historically, these bolts have an average thickness of 10.1 mm. A recent random sample of 10 bolts yielded these thicknesses: (Data EX0406) 9.7 9.9 10.3 10.1 10.5 9.4 9.9 10.1 9.7 10.3 (a) (1 point) Find the sample mean and standard deviation for these data.

what questionsStep-by-step explanation:...

Historically, these bolts have an average thickness

Ответ:

kayvontay4

20.01.2022

Mathematics

So, the sample mean is 9.99.

So, the standard deviation is 0.32.

Step-by-step explanation:

From Exercise we have the next numbers: 9.7 9.9 10.3 10.1 10.5 9.4 9.9 10.1 9.7 10.3.

So, N=10, because we have 10 numbers.

We calculate the sample mean:

$\overline{x}=\frac{9.7+ 9.9+ 10.3+ 10.1+ 10.5+ 9.4+ 9.9+ 10.1+ 9.7+ 10.3}{10}\\\\\overline{x}=\frac{99.9}{10}\\\\\overline{x}=9.99$

So, the sample mean is 9.99.

We use the formula for standard deviation:

$\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\overline{x})^2}$

Now, we calculate the sum

$\sum_{i=1}^{10}(x_i-9.99)^2=(9.7-9.99)^2+(9.9-9.99)^2+(10.3-9.99)^2+(10.1-9.99)^2+(10.5-9.99)^2+(9.4-9.99)^2+(9.9-9.99)^2+(10.1-9.99)^2+(9.7-9.99)^2+(10.3-9.99)^2\\\\\sum_{i=1}^{10}(x_i-9.99)^2=1.009$

Therefore, we get

$\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\overline{x})^2}\\\\\sigma=\sqrt{\frac{1}{10}\cdot 1.009}\\\\\sigma=0.32$

So, the standard deviation is 0.32.

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Historically, these bolts have an average thickness of 10.1 mm. A recent random sample of 10 bolts yielded these thicknesses: (Data EX0406) 9.7 9.9 10.3 10.1 10.5 9.4 9.9 10.1 9.7 10.3 (a) (1 point) Find the sample mean and standard deviation for these data.

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