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%.

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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

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

\/ \/ \/ \/

48 + 24 - 408 + 24 - 3

\ / \ /

72 - 432 - 3 = -363

Answer from: Quest

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative

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