Which ordered pair represents the solution to:

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

Yuri [45]

Answer:

(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.

(c) 0.15% of people has an IQ score greater than 139.

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.

5 0

3 years ago

Solve each quadratic equation by factoring with grouping. 5v2 – 18v = -9

djyliett [7]

Answer:

v = 3 , 3/5

Step-by-step explanation:

$5 {v}^{2} - 18v + 9 = 0 \\ 5 {v}^{2} - 3v - 15v + 9 = 0 \\ v(5v - 3) - 3(5v - 3) = 0 \\ (5v - 3)(v - 3) = 0 \\ v = 3 \\ v = \frac{3}{5}$

6 0

2 years ago

HELP ASAP PLEASEEEEEE

lord [1]

Answer:

The answer is 90 4/10

Step-by-step explanation:

if u divide 4 from 10 u will get 0.4

3 0

3 years ago

Read 2 more answers

Can Someone Please Help With my homework

Arada [10]

Answer:

10

Step-by-step explanation:

She already has 75 points. 140-75 is 65. 65/6.5 is 10.

5 0

2 years ago

What is the solution to 2sin^(2)x+sinx+1=0

Alexus [3.1K]

Well you can try rewriting it to this

answer is d 270

first start of by factoring and subtracting the 1 into the right side

sin(x) ( 2 sin (x) + 1) = -1

set each one equal to -1

sin( x) = -1 and 2 sin (x) +1 = -1

2 sin (x) = -2
sin ( x) = -1
so therefore we have our final equation

sin ( x ) = - 1 and sin (x) = -1

so then you look in your unit circle and find what coordinate equals -1 in terms of sin x

3 0

3 years ago