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Naily [24]
3 years ago
6

Suppose the number of inches of rainfall each year in a city is normally distributed. For a random sample of years, the confiden

ce interval (3.9,7.7) is generated. Find the margin of error Give just a number for your answer. For example, if you found that the margin of error was 2, you would enter 2.
Mathematics
1 answer:
Delvig [45]3 years ago
6 0

Answer:

Margin of error = 1.9 ≅2

Step-by-step explanation:

Given the number of inches of rainfall each year in a city is normally distributed.

For a random sample of years, the confidence interval (3.9,7.7) is generated

We know that the confidence intervals of margin of error is defined by

x⁻ ± margin of error

x⁻ ± M.E

Given the confidence intervals are (3.9 ,7.7)

Equating  lower limit  x⁻ -M.E = 3.9  …(i)

Equating  upper limit  x⁻ +M.E = 7.7 … (ii)

adding The equations (i) and (ii) and simplification , we get

2x⁻ = 11.6

Dividing by '2' on both sides , we get

x⁻ = 5.8

This is the mean of the sample x⁻ = 5.8

now substitute mean value in equation (i)

x⁻ -M.E = 3.9

5.8 - Margin of error = 3.9

Margin of error = 5.8 - 3.9

Margin of error = 1.9 ≅2

<u>Conclusion:</u>-

Margin of error = 1.9 ≅2

<u>Verification:-</u>

In given data  lower imit x⁻ -M.E = 3.9

we know that x⁻ = 5.8 and margin of error =2

5.8 -1.9 =3.9

3.9=3.9

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3 years ago
The brain volumes ​(cm cubed​) of 20 brains have a mean of 1111.2 cm cubed and a standard deviation of 125.3 cm cubed. Use the g
valentina_108 [34]

Answer:

Yes, the value 1411.8 cm³ is significantly high.

Step-by-step explanation:

Consider the provided information.

The brain volumes ​(cm cubed​) of 20 brains have a mean of 1111.2 cm cubed and a standard deviation of 125.3 cm cubed.

The range rule of thumb to identify the limits separating values that are significantly low or significantly high is:

The range rule of thumb identifying significant values are as.

Significantly low values are μ-2σ

Substitute the μ = 1111.2 and σ = 125.3 in above formula.

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Significantly high values are μ+2σ

Substitute the μ = 1111.2 and σ = 125.3 in above formula.

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The value is significantly high due to the value 1411.8 cm³ is not lie between the values 860.6 cm³ and 1361.8 cm³.

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