Two similar triangles are shown on the coordinate grid:

Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and an

Daniel [21]

Using the normal distribution, the percentages are given as follows:

a) 9.18%.

b) 97.72%.

c) 50%.

d) 4.27%.

e) 0.13%.

f) 59.29%.

g) 2.46%.

h) 50%.

i) 50%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For this problem, the mean and the standard deviation are given as follows:

$\mu = 247, \sigma = 60$

For item a, the proportion is the <u>p-value of Z when Z = 167</u>, hence:

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

Z = (167 - 247)/60

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

Hence the percentage is of 9.18%.

For item b, the proportion is the <u>p-value of Z when Z = 367</u>, hence:

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

Z = (367 - 247)/60

Z = 2.

Z = 2 has a p-value of 0.9772.

Hence the percentage is of 97.72%.

For item c, the proportion is <u>one subtracted by the p-value of Z when X = 247</u>, hence:

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

Z = (247 - 247)/60

Z = 0

Z = 0 has a p-value of 0.5.

Hence the percentage is of 50%.

For item d, the proportion is <u>one subtracted by the p-value of Z when X = 350</u>, hence:

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

Z = (350 - 247)/60

Z = 1.72

Z = 1.72 has a p-value of 0.9573.

1 - 0.9573 = 0.0427.

Hence the percentage is of 4.27%.

For item e, the proportion is the <u>p-value of Z when Z = 67</u>, hence:

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

Z = (67 - 247)/60

Z = -3.

Z = -3 has a p-value of 0.0013.

Hence the percentage is of 0.13%.

For item f, the proportion is the <u>p-value of Z when X = 300 subtracted by the p-value of Z when X = 200</u>, hence:

X = 300:

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

Z = (300 - 247)/60

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

X = 200:

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

Z = (200 - 247)/60

Z = -0.78.

Z = -0.78 has a p-value of 0.2177.

0.8106 - 0.2177 = 0.5929.

Hence the percentage is 59.29%.

For item g, the proportion is the <u>p-value of Z when X = 400 subtracted by the p-value of Z when X = 360</u>, hence:

X = 400:

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

Z = (400 - 247)/60

Z = 2.55.

Z = 2.55 has a p-value of 0.9946.

X = 360:

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

Z = (360 - 247)/60

Z = 1.88.

Z = 1.88 has a p-value of 0.97.

0.9946 - 0.97 = 0.0246

Hence the percentage is 2.46%.

For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.

More can be learned about the normal distribution at brainly.com/question/24808124

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$352,590 is the interest rate on Malik’s savings account for four years

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If Mrs garcia maintains a constant speed, consistent with the results above, how many words can she type in 49 minutes

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Read 2 more answers

The value of y varies directly as the square of x and y=-12 when x=2. What is y when x=-4?

lesya [120]

The value of y varies directly as the square of x and y = -12 when x = 2 then the value of y when x = -4 exists y = 24.

<h3>What is meant by direct variation?</h3>

When two variable quantities contain a constant ratio, their relationship exists comprehended a direct variation. It exists said that one variable varies directly as the other. The formula for direct variation is y = kx, where k exists the constant of variation.

The constant value (often written k) relating amounts that rise or fall uniformly together. It exists the ratio of the amounts y and x:

k = y/x.

Put another way: y = kx.

Accordingly, the equation has the form y = kx, where k may be any number.

Substituting y = -12 when x = 2, we get

-12 = k × 2

simplifying the above equation, we get

⇒ k = -6

Therefore, the required equation exists y = -6x.

The value of y when x = -4 is y = -6 × -4 = 24.

To learn more about direct variation refer to:

brainly.com/question/6499629

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3 0

1 year ago