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kaheart [24]
2 years ago
9

NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6 6 . In an earlier s

tudy, the population proportion was estimated to be 0.32 0.32 . How large a sample would be required in order to estimate the fraction of people who black out at 6 6 or more Gs at the 85% 85 % confidence level with an error of at most 0.03 0.03 ? Round your answer up to the next integer.
Mathematics
1 answer:
Xelga [282]2 years ago
3 0

Answer:

The sample size must be atleast 502 to have a margin of error of 0.03

Step-by-step explanation:

We are given the following in the question:

Proportion = 0.32

\hat{p} = 0.32

Level of significance = 0.15

Margin of error = 0.03

Formula for margin of error =

z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.15} = 1.44

We have to find the sample size such that the margin of error is atmost 0.03.

Putting values, we get,

z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\leq 0.03\\\\1.44\times \sqrt{\dfrac{0.32(1-0.32)}{n}}\leq 0.03\\\\\sqrt{n}\geq 1.44\times \dfrac{\sqrt{0.32(1-0.32)}}{0.03}\\\\\sqrt{n}\geq 22.39\\n\geq 501.3121\\\Rightarrow n\geq 502

Thus, the sample size must be atleast 502 to have a margin of error of 0.03 in approximation of proportion of people who would black out at 6 or more Gs.

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Anton [14]

Answer:

Let x be the total number of cupcakes.

Chocolate chips =

\frac{2}{3} x

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\frac{1}{4}  \times  \frac{1}{3}  \\  =  \frac{1}{12} x

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given

\frac{1}{4} x = 90

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8 0
3 years ago
Find the interior angle sum for the following polygon
Brrunno [24]

Answer:

Polygon Name  

Number of Interior Angles  

Sum of Interior Angles = (n-2) x 180°  

Triangle  

3  

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Quadrilateral  

4  

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<u><em> Pentagon  </em></u>

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Step-by-step explanation:

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Read 2 more answers
Segment PE has endpoints P(-4,4) and E(0,-4). Find the coordinates of point Q such that PQ:QE is 1:3. Enter the coordinates belo
Natalka [10]

Answer:

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Step-by-step explanation:

Given that point Q, partitions segment PE, such that PQ:QE is 1:3, coordinates of point Q is found using the formula below:

x = \frac{mx_2 + nx_1}{m + n}

y = \frac{my_2 + ny_1}{m + n}

Where,

P(-4, 4) = (x_1, y_1)

E(0, -4) = (x_2, y_2)

m = 1, n = 3

Plug in the necessary values to find x and y coordinates for point Q as follows:

x = \frac{mx_2 + nx_1}{m + n}

x = \frac{1(0) + 3(-4)}{1 + 3}

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x = \frac{-12}{4}

x = -3

y = \frac{my_2 + ny_1}{m + n}

y = \frac{1(-4) + 3(4)}{1 + 3}

y = \frac{-4 + 12}{4}

y = \frac{8}{4}

y = 2

The coordinates of the point Q are (-3, 2))

8 0
3 years ago
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