Mathematics, 16.07.2021 01:00 eggg65

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. (a) Find the IQ scores that represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
(c) Find the IQ score for the top 5%.

Answers: 2

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Answers

Answer from: andrecoral105

a) IQ scores of 94.2 and below represent the bottom 35%.

b) An IQ score of 110.1 represents the 3rd quartile.

c) IQ scores of 124.7 and higher are in the top 5%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 100 and a standard deviation of 15.

This means that $\mu = 100, \sigma = 15$

(a) Find the IQ scores that represent the bottom 35%.

The 35th percentile and below, in which the 35th percentile is X when Z has a p-value of 0.35, so X when Z = -0.385.

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

$-0.385 = \frac{X - 100}{15}$

X - 100 = -0.385*15

X = 94.2

IQ scores of 94.2 and below represent the bottom 35%.

(b) Find the IQ score that represents the 3rd Quartile.

This is the 100*3/4 = 75th percentile, which is X when Z has a p-value of 0.75, so X when Z = 0.675.

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

$0.675 = \frac{X - 100}{15}$

X - 100 = 0.675*15

X = 110.1

An IQ score of 110.1 represents the 3rd quartile.

IQ scores of 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.

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

$1.645 = \frac{X - 100}{15}$

X - 100 = 1.645*15

X = 124.7

IQ scores of 124.7 and higher are in the top 5%.

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

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000