Solve:<br> (7 + 18) + (3 X 6) + (4 x 5) =

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

Find the roots of f(x)=x^2+10x−96

a_sh-v [17]

Answer:

x = -16 or x = 6

Step-by-step explanation:

To find the roots of a polynomial function, set the polynomial equal to zero and solve for x.

x² + 10x - 96 = 0

We need to factor the left side. The left side is a quadratic polynomial whose first coefficient is 1. We need two numbers whose product is -96 and whose sum is 10. The numbers are 16 and -6.

(x + 16)(x - 6) = 0

If a product of two factors equals zero, then one factor or the other or both must equal zero.

x + 16 = 0 or x - 6 = 0

x = -16 or x = 6

6 0

3 years ago

7x+7+2z+9= please help me

fiasKO [112]

Answer:

7x+2z+16

Step-by-step explanation:

find like terms

7 9

add them

7+9=16

7x+2z+16

8 0

3 years ago

Mark drank 3 2/5 cups of orange jucie in the morning and 2 1/5 cups in the afternoon. How much orange jucie did mark drink in al

Alinara [238K]

Solutions

1) Convert mixed fractions into improper fractions.

$\frac{17}{5}+ \frac{11}{5}$

$= ((17 * 5) + (11 * 5)) / (5 * 5)$

$= (85 + 55) / 25$

$= 140/25$

$= 28/5$

$5 \frac{3}{5}$

5 0

3 years ago

(x ^ 2 - 4x + 7)(2x - 2)

Marat540 [252]

Simplify the expression.

2x^3-10x^2+22x-14

3 0

3 years ago

Solve: (7 + 18) + (3 X 6) + (4 x 5) =