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Elodia [21]
3 years ago
13

A sample of 56 research cotton samples resulted in a sample average percentage elongation of 8.63 and a sample standard deviatio

n of 0.79. calculate a 95% large-sample ci for the true average percentage elongation μ. (give answers accurate to 2 decimal places.)
Mathematics
1 answer:
ss7ja [257]3 years ago
5 0

To solve for the confidence interval for the true average percentage elongation, we use the z statistic. The formula for confidence interval is given as:

Confidence interval = x ± z σ / sqrt (n)

where,

x = the sample mean = 8.63

σ = sample standard deviation = 0.79

n = number of samples = 56

 

From the standard distribution tables, the value of z at 95% confidence interval is:

z = 1.96

 

Therefore substituting the known values into the equation:

Confidence interval = 8.63 ± (1.96) (0.79) / sqrt (56)

Confidence interval = 8.63 ± 0.207

Confidence interval = 8.42, 8.84

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3 years ago
Simplify this radical
Lady_Fox [76]

The given radical root 84, the simplification is option B; 2\sqrt{21}.

<h3>What is a simplification of an expression?</h3>

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given radical;

\sqrt{84} \\\\\sqrt{42 \times 2} \\\\\sqrt{7\times3\times 2 \times 2} \\\\2\sqrt{21} \\

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6 0
2 years ago
The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0 (Think of these as
bija089 [108]

Answer:

0.477 is  the probability that the average score of the 36 golfers was between 70 and 71.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 70

Standard Deviation, σ = 3

Sample size, n = 36

Let the average score of all pro golfers follow a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(score of the 36 golfers was between 70 and 71)

\text{Standard error of sampling} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{36}} = \frac{1}{2}

P(70 \leq x \leq 71) = P(\displaystyle\frac{70 - 70}{\frac{3}{\sqrt{36}}} \leq z \leq \displaystyle\frac{71-70}{\frac{3}{\sqrt{36}}}) = P(0 \leq z \leq 2)\\\\= P(z \leq 2) - P(z \leq 0)\\= 0.977 - 0.500 = 0.477= 47.7\%

P(70 \leq x \leq 71) = 47.7\%

0.477 is  the probability that the average score of the 36 golfers was between 70 and 71.

8 0
4 years ago
Write an equation for the line that passes through the points (-1,-12) and (4,8)​
Aleks [24]

Answer:

y = 4x - 8

Step-by-step explanation:

(-1, -12) & (4, 8)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(8 - (-12)) / (4 - (-1))

Simplify the parentheses.

= (8 + 12) / (4 + 1)

= (20) / (5)

Simplify the fraction.

20/5

= 4

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (4, 8). Plug in the x and y values into the x and y of the standard equation.

8 = 4(4) + b

To find b, multiply the slope and the input of x(4)

8 = 16 + b

Now, subtract 16 from both sides to isolate b.

-8 = b

Plug this into your standard equation.

y = 4x - 8

This is your equation.

Check this by plugging in the other point you have not checked yet (-1, -12).

y = 4x - 8

-12 = 4(-1) - 8

-12 = -4 - 8

- 12 = -12

Your equation is correct.

Hope this helps!

8 0
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Alika [10]

Answer:2 feet 4 inches more; 28 inches

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48-20=28 inches

6 0
3 years ago
Read 2 more answers
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