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nirvana33 [79]
3 years ago
9

EXPLAIN THE ERROR Cody was given two points (1/2,4) and (2/3,1), on a line and asked to create a linear equation in standard for

m. Cody’s work in shown. Identify any errors and correct them

Mathematics
1 answer:
inessss [21]3 years ago
6 0

Answer:

Cody made a mistake when calculating the slope of the line and this affected every other steps after than.

She divided -3 by 6 instead of -3 by 1/6

Step-by-step explanation:

Given

(x_1,y_1) = (\frac{1}{2},4)

(x_2,y_2) = (\frac{2}{3},1)

<em>See attached for steps</em>

Required

Explain Cody's error

<em>Cody made a mistake when calculating the slope of the line and this affected every other steps after than.</em>

See Proof

Slope (m) is calculated as thus:

m =\frac{y_2 - y_1}{x_2 - x_1}

m =\frac{1 - 4}{\frac{2}{3} - \frac{1}{2}}

m =-\frac{ 3}{\frac{1}{6}}

m = -3/\frac{1}{6}

m = -3 * 6

m = -18

This is in contrast to m = -\frac{1}{2}, calculated by Cody

Solving further to determine the equation.

y - y_1 = m(x - x_1)

Where

(x_1,y_1) = (\frac{1}{2},4)

m = -18

y - 4 = -18(x - \frac{1}{2})

y - 4 = -18x + 9

Collect Like Terms

y + 18x = 9 + 4

y + 18x = 13

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a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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In this problem:

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  • A sample of 150 couples is taken, hence n = 150.

Item a:

The mean and the standard error are given by:

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s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338

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Item b:

The probability is <u>one subtracted by the p-value of Z when X = 0.25</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem:

Z = \frac{X - \mu}{s}

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Item c:

The probability is the <u>p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15</u>, hence:

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To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213

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