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vlada-n [284]
3 years ago
5

A population is known to be normally distributed with a standard deviation of 2.8. (a) Compute the 95% confidence interval on th

e mean based on the following sample of nine: 8, 9, 10, 13, 14, 16, 17, 20, 21. (b) Now compute the 99% confidence interval using the same data.
Mathematics
1 answer:
Ugo [173]3 years ago
3 0

Answer:

Step-by-step explanation:

Mean = sum of terms/number of terms

The mean of the given sample is

(8 + 9 + 10 + 13 + 14 + 16 + 17 + 20 + 21)/9 = 14.2

a)

For a confidence level of 95%, the corresponding z value is 1.96.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

Where

n represents the number of samples

It becomes

14.2 ± 1.96 × 2.8/√9

= 14.2 ± 1.96 × 0.933

= 14.2 ± 1.83

The lower end of the confidence interval is 12.37

The upper end of the confidence interval is 16.03

b)

For a confidence level of 99%, the corresponding z value is 2.58

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

Where

n represents the number of samples

It becomes

14.2 ± 2.58 × 2.8/√9

= 14.2 ± 2.58 × 0.933

= 14.2 ± 2.4

The lower end of the confidence interval is 11.8

The upper end of the confidence interval is 16.6

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3 years ago
A circle has a circumference of 28π centimeters. In terms of π, what is the area of the circle to the nearest square centimeter?
Vadim26 [7]

Hi there!

The formula to find the are of a circle is :

a = \pir²

The formula to find the circumference of a circle is :

c = 2\pir


In order to use the area formula, you need to figure out what the radius (r) is.

If we solve for "r" in the circumference equation, we have :

r = c ÷ (2\pi)


Now we use this to replace "r" in the area formula :

a = \pi ( c ÷ (2\pi))²


When we simplify this we get :

a = c² ÷ 4\pi


Now you can put your value of "c" into this equation and find "a".

*Remember, \pi is about 3.1416.


Solving for "a" :

a = c² ÷ 4\pi

a = 28² ÷ 4\pi


28² = 28 × 28 = 784


a = 784 ÷ 4\pi


4\pi = 4 × \pi = 12.56637061435917


a = 784 ÷ 12.56637061435917

a = 62.38873769202297cm²


You need to round to the nearest square centimeter, which means that you need to round to the nearest whole number :

a = 62cm²


There you go! I really hope this helped, if there's anything just let me know! :)

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