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nordsb [41]
3 years ago
7

Use the composite below to mark each statement as true or false.justify your choices.​

Mathematics
1 answer:
Masja [62]3 years ago
3 0
Hi sorry but what’s the answer choices if they have them I’m not trying to just get points are anything but what’s the answer choices ?
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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

#SPJ1

4 0
2 years ago
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