Mathematics, 21.06.2020 05:57 coltonsteighner

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1521 and the standard deviation was 314. The test scores of four students selected at random are 1920, 1290, 2220, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual

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Answer from: realpcy7515

A score of 1920 has a z-score of 1.27.

A score of 1290 has a z-score of -0.74.

A score of 2220 has a z-score of 2.23.

A score of 1420 has a z-score of -0.32.

The score of 2220 is more than two standard deviations from the mean, so it is unusual.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is 2 or more standard deviations from the mean, it is considered unusual.

In this question, we have that:

$\mu = 1521, \sigma = 314$

Score of 1920:

X = 1920. Then

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

$Z = \frac{1920 - 1521}{314}$

Z = 1.27

A score of 1920 has a z-score of 1.27.

Score of 1290:

X = 1290. Then

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

$Z = \frac{1290 - 1521}{314}$

Z = -0.74

A score of 1290 has a z-score of -0.74.

Score of 2220:

X = 1290. Then

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

$Z = \frac{2220 - 1521}{314}$

Z = 2.23

A score of 2220 has a z-score of 2.23.

Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.

Score of 1420:

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

$Z = \frac{1420 - 1521}{314}$

Z = -0.32

A score of 1420 has a z-score of -0.32.

Answer from: Quest

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

In the diagram of circle o, what is the measure of abc? 210 150

Answer from: Quest

i would be happy to . most people on would also love to i'm sure. if you just want someone who has done algebra before and want a little more personal relationship than just begging strangers for , i can certainly be of service. i do have college myself so i might not be 24/7.

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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 152...