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son4ous [18]
3 years ago
14

A population proportion is . A sample of size will be taken and the sample proportion will be used to estimate the population pr

oportion. Use z-table. Round your answers to four decimal places. Do not round intermediate calculations. a. What is the probability that the sample proportion will be within of the population proportion? b. What is the probability that the sample proportion will be within of the population proportion?
Mathematics
1 answer:
katen-ka-za [31]3 years ago
4 0

Complete Question:

A population proportion is 0.4. A sample of size 200 will be taken and the sample proportion p will be used to estimate the population proportion. Use z- table Round your answers to four decimal places. Do not round intermediate calculations. a. What is the probability that the sample proportion will be within ±0.03 of the population proportion? b. What is the probability that the sample proportion will be within ±0.08 of the population proportion?

Answer:

A) 0.61351

Step-by-step explanation:

Sample proportion = 0.4

Sample population = 200

A.) proprobaility that sample proportion 'p' is within ±0.03 of population proportion

Statistically:

P(0.4-0.03<p<0.4+0.03)

P[((0.4-0.03)-0.4)/√((0.4)(.6))/200 < z < ((0.4+0.03)-0.4)/√((0.4)(.6))/200

P[-0.03/0.0346410 < z < 0.03/0.0346410

P(−0.866025 < z < 0.866025)

P(z < - 0.8660) - P(z < 0.8660)

0.80675 - 0.19325

= 0.61351

B) proprobaility that sample proportion 'p' is within ±0.08 of population proportion

Statistically:

P(0.4-0.08<p<0.4+0.08)

P[((0.4-0.08)-0.4)/√((0.4)(.6))/200 < z < ((0.4+0.08)-0.4)/√((0.4)(.6))/200

P[-0.08/0.0346410 < z < 0.08/0.0346410

P(−2.3094 < z < 2.3094)

P(z < -2.3094 ) - P(z < 2.3094)

0.98954 - 0.010461

= 0.97908

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

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∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

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14x=x^2-15<br><br> find the value of x
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