Mathematics, 07.04.2020 18:54 allysoftball6226

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.

a. Give the distribution of X
b. Find the probability that the person has an IQ greater than 130, write the probability statement. What is the probability? (round your answer to the four decimal places.)
c. Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.

Write the probability statement.

P(X > x) =

What is the minimum IQ? (Round your answer to the nearest whole number.)
x =
Sketch the graph

d. The middle 20% of IQs fall between what two values?

Write the probability statement.
P(x1 < X < x2) =

State the two values. (Round your answers to the nearest whole number.)
x1=x2=
Sketch the graph

Answers: 2

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Answers

Answer from: sheyunicorn

(a) The distribution of X is N (100, 15²).

(b) The probability that a person has an IQ greater than 130 is 0.0228.

(d) The middle 20% of IQs fall between 96 and 104.

Step-by-step explanation:

The random variable X is defined as the IQ of an individual.

(a)

The random variable X is normally distributed with mean, μ = 100 and standard deviation, σ = 15.

The probability density function of X is:

$f_{X}(x)=\frac{1}{15\sqrt{2\pi}}\times e^{-(x-100)^{2}/(2\times 15^{2})};\ -\infty$

Thus, the distribution of X is N (100, 15²).

(b)

Compute the probability that a person has an IQ greater than 130 as follows:

$P(X130)=P(\frac{X-\mu}{\sigma}\frac{130-100}{15})$

$=P(Z2)\\=1-P(Z$

Thus, the probability that a person has an IQ greater than 130 is 0.0228.

(c)

Let x represents the top 2% of all IQs.

Then, P (X > x) = 0.02.

⇒ P (X < x) = 1 - 0.02

⇒ P (Z < z) = 0.98

The value of z is:

z = 2.06.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\2.06=\frac{x-100}{15}\\x=100+(2.06\times 15)\\x=130.9\\x\approx131$

Thus, the minimum IQ needed to qualify for the Mensa organization is 131.

(d)

Let x₁ and x₂ be the values between which middle 20% of IQs fall.

This implies that:

$P(x_{1}$

The value of z is:

z = 0.26.

Compute the value of x as follows:

$-z=\frac{x_{1}-\mu}{\sigma}\\-0.26=\frac{x_{1}-100}{15}\\x_{1}=100-(0.26\times 15)\\x=96.1\\x\approx96$ $z=\frac{x_{2}-\mu}{\sigma}\\0.26=\frac{x_{2}-100}{15}\\x_{2}=100+(0.26\times 15)\\x=103.9\\x\approx104$

Thus, the middle 20% of IQs fall between 96 and 104.

Answer from: Quest

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)

Find the measure of the missing angle pls me plsssss

Answer from: Quest

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?