Mathematics, 17.08.2019 17:20 iyana479

Scores of an iq test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. use the empirical rule to determine the following. (a) what percentage of people has an iq score between 87 and 113? (b) what percentage of people has an iq score less than 74 or greater than 126? (c) what percentage of people has an iq score greater than 139?

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Answer from: rrgg6234

68% percent of people has an IQ score between 87 and 113, 5% percent of people has an IQ score less than 74 or greater than 126, and 0.15% percent of people has an IQ score greater than 139 and this can be determined by using the empirical rule.

Given :

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13.

Empirical rule said that:

68% of data lies between $\rm \bar{x} - \sigma$ and $\rm \bar{x} + \sigma$ .

95% of data lies between $\rm \bar{x} - 2\sigma$ and $\rm \bar{x} + 2\sigma$ .

99.7% of data lies between $\rm \bar{x} - 3\sigma$ and $\rm \bar{x} + 3\sigma$ .

$\rm \bar{x} - \sigma$ = 100 - 13 = 87

$\rm \bar{x} + \sigma$ = 100 + 13 = 113

[ $\rm \bar{x} - \sigma$ , $\rm \bar{x} + \sigma$ ] = [87 , 113]

68% of people have an IQ score between 87 and 113.

$\rm \bar{x} - 2\sigma$ = 100 - 26 = 74

$\rm \bar{x} + 2\sigma$ = 100 + 26 = 126

[ $\rm \bar{x} - 2\sigma$ , $\rm \bar{x} + 2\sigma$ ] = [74 , 126]

95% of people have an IQ score between 74 and 126.

The percentage of people who have an IQ score less than 74 or greater than 126 is:

P = 100 - 95

P = 5%

$\rm \bar{x} - 3\sigma$ = 100 - 39 = 61

$\rm \bar{x} + 3\sigma$ = 100 + 39 = 139

[ $\rm \bar{x} - 3\sigma$ , $\rm \bar{x} + 3\sigma$ ] = [61 , 139]

99.7% of people have an IQ score between 61 and 139.

The percentage of people who have an IQ score less than 61 or greater than 139 is:

P = 100 - 99.7

P = 0.3%

The percentage of people who have an IQ score greater than 139 is:

P = 0.5 (0.3)

P = 0.15%

0.15% percentage of people has an IQ score greater than 139.

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Answer from: asaadasaadasaad6524

(a) 68% of people has an IQ score between 87 and 113.

(b) 5% of people has an IQ score less than 74 or greater than 126.

Step-by-step explanation:

Given information:Scores of an IQ test have a bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between $\overline{x}-\sigma$ and $\overline{x}+\sigma$ .

95% data lies between $\overline{x}-2\sigma$ and $\overline{x}+2\sigma$ .

99.7% data lies between $\overline{x}-3\sigma$ and $\overline{x}+3\sigma$ .

(a)

$\overline{x}-\sigma=100-13=87$

$\overline{x}+\sigma=100+13=113$

$[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]$

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113.

(b)

$\overline{x}-2\sigma=100-2(13)=74$

$\overline{x}+2\sigma=100+2(13)=126$

$[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]$

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126.

P = 1- 95%

P = 5%

Therefore 5% of people has an IQ score less than 74 or greater than 126.

(c)

$\overline{x}-3\sigma=100-3(13)=61$

$\overline{x}+3\sigma=100+3(13)=139$

$[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]$

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139 is

$P=\frac{1}{2}(0.3\%)=0.15\%$

Therefore 0.15% of people has an IQ score greater than 139.

Answer from: Quest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

Answer from: Quest

Step by step expontion

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