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Fudgin [204]
3 years ago
14

An SRS of 2,500 individuals was taken from a large city to estimate the percentage of city residents with a graduate degree. 555

people in the sample had a graduate degree. The percentage of individuals in the city with a graduate degree is estimated as 22.2%. The estimated standard error is closest to:_______a. 1%b. 10% c. 0.1%
Mathematics
1 answer:
Luden [163]3 years ago
7 0

Answer:

The option is  b

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  2500

   The number with a graduate degree is  k =  555

    The sample  proportion is \^ p = 0.222

Generally the standard error is mathematically represented as

           SE = \sqrt{\frac{\^ p (1- \^ p )}{n} }

=>        SE = \sqrt{\frac{0.222 (1- 0.22 )}{2500 } }

=>        SE = 0.010

Converting to percentage

           SE = 0.010 * 100

=>       SE =10\%

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Answer:

A) Length = 110.4 mm and width = 62.1 mm

B) A = 6855.84 mm²

C) length = 114.7 mm

width = 55.8 mm

Area = 6400.26 mm²

D) Screen with aspect ratio of 16:9 is bigger

Step-by-step explanation:

A) We are told that the aspect ratio of the phone screen = 16:9. This means that the ratio of the length to the width of the screen is 16:9.

To find the side length, we will say that;

length = 16x

width = 9x

Thus, since the edges are perpendicular, then we can use pythagoras theorem since we know that the diagonal is 127 mm

Thus;

(16x)² + (9x²)] = 127²

256x² + 81x² = 16129

337x² = 16129

x² = 16129/337

x = √(16129/337)

x = 6.9

Thus;

length = 16x = 16 × 6.9 = 110.4 mm

width = 9x = 9 × 6.9 = 62.1 mm

Length = 110.4 mm and width = 62.1 mm

B) area of screen is;

A = length × width

A = 110.4 × 62.1

A = 6855.84 mm²

C) We are told that the aspect ratio is now 18.5:9.

Thus;

length = 18.5x

width = 9x

Thus;

(18.5x)² + (9x²)] = 127²

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423.25x² = 16129

x² = 16129/423.25

x = √(16129/423.25)

x = 6.2

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width = 9x = 9 × 6.2 = 55.8 mm

Area = 114.7 × 55.8 = 6400.26 mm²

D) Screen with aspect ratio of 16:9 is bigger

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