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2 years ago

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1 answer:

zheka24 [161]2 years ago

6 0

Step-By-Step Explanation:

1. 20.95 x 1 = 20.95

2. 119.5 x 2 = 239

3. 8.75 x 5 = 77.5

4. 24.25 x 7 = 169.75

5. 52.3 x 3 = 156.9

6. 0.4

7. 0.4

8. 0.4

9. 0.7

10. 0.5

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A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard d

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The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]

<h3>
How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>

Suppose that we have:

Sample size n > 30
Sample mean = $\overline{x}$
Sample standard deviation = s
Population standard deviation = $\sigma$
Level of significance = $\alpha$

Then the confidence interval is obtained as

Case 1: Population standard deviation is known

$\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}$

Case 2: Population standard deviation is unknown.

$\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}$

For this case, we're given that:

Sample size n = 90 > 30
Sample mean = $\overline{x}$ = 138
Sample standard deviation = s = 34
Level of significance = $\alpha$ = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).

At this level of significance, the critical value of Z is: $Z_{0.1/2}$ = ±1.645

Thus, we get:

$CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]$

Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]

Learn more about confidence interval for population mean from large samples here:

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2 years ago

Given the vectors w = <-5, 3> and z = <1, 4>, find the results of the vector subtractions. -w − z = z − w = w − z =

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Answer:

-w − z = <4, -7>

z − w = <6, 1>

w − z = <-6, -1>

Step-by-step explanation:

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2 years ago

M=-(4+m)+2

andrezito [222]

m=-(4+m)+2
m=-4-m+2
m+m=-4+2
2m=-2
m=-2/2
m=-1

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4 years ago

If g(x)=2x + 1, find g(a + h)- g(a). 2h 2h + 2 h + 1

katovenus [111]

G(x) = 2x + 1

Find g(a + h):
g(a + h) = 2(a + h) + 1 = 2a + 2h + 1

Find g(a):
g(a) = 2(a) + 1 = 2a + 1

Find g(a + h) - g(a):
g(a + h) - g(a) = 2a + 2h + 1 - ( 2a + 1)

Distribute the negative sign:
g(a + h) - g(a) = 2a + 2h + 1 - 2a - 1

Combine like terms:
g(a + h) - g(a) = 2h

Answer: 2h

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4 years ago

Marge drive 290 miles in five hours. Three hours were on the interstate, then the remainder of the trip was on a road that cause

vivado [14]

Marge drove by 66 miles per hour on the interstate

Step-by-step explanation:

Marge drive 290 miles in five hours, her trip has two stages

She drove 3 hours on the interstate
The remainder of the trip was on a road that caused her to reduce her speed by 20 mph

We need to find how fast Marge drove on the interstate

Assume that she drove by speed x miles per hour on interstate

∵ Distance = speed × time

∵ Her speed on the interstate is x mph

∵ The time of interstate is 3 hours

∴ The distance of interstate = x × 3 = 3x miles

∵ The time of the total trip is 5 hours

∵ She spent 3 hours on the interstate

∴ The time of the remainder of the trip = 5 - 3 = 2 hours

∵ She reduced her speed 20 mph for the remainder of the trip

∴ Her speed on the remainder of the trip = x - 20 mph

∴ The remainder distance = (x - 20) × 2

∴ The remainder distance = 2x - 40 miles

∵ The total distance of the trip is 290 miles

- Equate the sum of the two distances above by 290

∴ 3x + 2x - 40 = 290

- Add the like terms in the left hand side

∴ 5x - 40 = 290

- Add 40 to both sides

∴ 5x = 330

- Divide both sides by 5

∴ x = 66

Marge drove by 66 miles per hour on the interstate

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