Mathematics, 30.09.2019 04:00 mg0508092

Scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. what is the minimum score you would need to be in the top 5%?

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Answer from: 7obadiah

Using the normal distribution, it is found that the minimum score to be in the top 5% is of 86.4.

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In a normal distribution, the z-score is used.

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

$\mu$ is the mean and $\sigma$ is the standard deviation.It measures how many standard deviations the measure is from the mean. Each z-score has an associated p-value, which is the percentile of the measure X.

In this problem:

Mean of 76.4, thus $\mu = 76.4$ Standard deviation of 6.1, thus $\sigma = 6.1$ The top 5% is at least the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.

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

$1.645 = \frac{X - 76.4}{6.1}$

X - 76.4 = 6.1(1.645)

X = 86.4

The minimum score needed to be in the top 5% is of 86.4.

A similar problem is given at link

Answer from: Jvnvthvn

The top 5% of scores belong to the 95th percentile, which means the cutoff score

is such that

$\mathbb P(X$

Transforming to the standard normal distribution, you have

$\mathbb P(X$

A left-tail probability of 95% corresponds to a z-score of about k^*=1.6449

, which means the cutoff score must be around

$1.6449=\dfrac{k-76.4}{6.1}\implies k\approx86.4$

Answer from: Quest

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.

Answer from: Quest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

$\frac{ab}{bc} =\frac{ad}{ab}$

now, we can cross multiply

and we get

$ab\timesab=ad\times bc$

$ab^2=ad\times bc$

so, this could be step to prove it

Seth is using the figure shown below to prove pythagorean theorem using triangle similarity: in the

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