1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Valentin [98]
3 years ago
14

Assume that adults have IQ scores that are normally distributed with a mean of 95.9 and a standard deviation of 16.4. Find the f

ollowing probabilities. Round your answers to three decimal places; add trailing zeros as needed. The probability that a randomly selected adult has an IQ greater than 122.6 is 0.052 . The probability that a randomly selected adult has an IQ lower than 92.0 is 0.413 . The probability that a randomly selected adult has an IQ between 80.0 and 110.0 is 0.639 .
Mathematics
1 answer:
mote1985 [20]3 years ago
3 0

Answer:

a) The probability that a randomly selected adult has an IQ greater than 122.6 is 0.052.

b) The probability that a randomly selected adult has an IQ lower than 92.0 is 0.405.

c) The probability that a randomly selected adult has an IQ between 80.0 and 110.0 is 0.639.

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 95.9

Standard deviation = σ = 16.4

a) The probability that a randomly selected adult has an IQ greater than 122.6

= P(x > 122.6)

We first normalize or standardize 122.6

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (122.6 - 95.9)/16.4 = 1.63

To determine the required probability

P(x > 122.6) = P(z > 1.63)

We'll use data from the normal distribution table for these probabilities

P(x > 122.6) = P(z > 1.63) = 1 - P(z ≤ 1.63)

= 1 - 0.94845

= 0.05155 = 0.052 to 3 d.p

b) The probability that a randomly selected adult has an IQ lower than 92.0 = P(x < 92)

We first normalize or standardize 92.0

z = (x - μ)/σ = (92 - 95.9)/16.4 = - 0.24

To determine the required probability

P(x < 92.0) = P(z < -0.24)

We'll use data from the normal distribution table for these probabilities

P(x < 92.0) = P(z < -0.24) = 0.40517 = 0.405 to 3 d.p

c) The probability that a randomly selected adult has an IQ between 80.0 and 110.0.

P(80 ≤ x ≤ 110)

We first normalize or standardize 80.0 and 110.0

For 80.0

z = (x - μ)/σ = (80 - 95.9)/16.4 = - 0.97

For 110.0

z = (x - μ)/σ = (110 - 95.9)/16.4 = 0.86

The required probability

P(80 ≤ x ≤ 110) = P(-0.97 ≤ z ≤ 0.86)

We'll use data from the normal distribution table for these probabilities

(80 ≤ x ≤ 110) = P(-0.97 ≤ z ≤ 0.86)

= P(z ≤ 0.86) - P(z ≤ -0.97)

= 0.80511 - 0.16602

= 0.63909 = 0.639 to 3 d.p

Hope this Helps!!!

You might be interested in
plesee help me do I need it under 25min and don't answer if you don't know or else u will be reported thank you (◔‿◔)​
34kurt

Answer:

l = 2.25 cm

Step-by-step explanation:

given l is inversely proportional to w² then the equation relating them is

l = \frac{k}{w^2} ← k is the constant of proportion

(i)

to find k use the condition w = 1.5 , l = 16 , then

16 = \frac{k}{1.5^2} = \frac{k}{2.25} ( multiply both sides by 2.25 )

36 = k

l = \frac{36}{w^2} ← equation of proportion

(ii)

when w = 4 , then

l = \frac{36}{4^2} = \frac{36}{16} = 2.25 cm

3 0
1 year ago
Graph the following Line:<br> 6x+3y=6
yulyashka [42]

Answer:

Visit geogebra.com

Step-by-step explanation:

none needed <3

8 0
2 years ago
Read 2 more answers
3 pizzas are shared equally between 10 people. What fraction of a pizza does each person receive?
kifflom [539]

Answer:

7

Step-by-step explanation:

and beetween 10-3 7 pizza

7 0
3 years ago
How many cones of radius 1 m and height 1 m have total volume equal to the volume of a sphere with a radius 1m?
DiKsa [7]
Vcone=1/3(hpir^2)
Vsphere=(4/3)pir^3

evaluate
vcone=1/3(1pi1^2)=pi/3
vsphere=4/3pi1^3=4pi/3


pi/3 times what=4pi/3
times both sides by 3
pi times what=4pi
divide both sides by pi
1 times what=4
what=4



4 cones

7 0
3 years ago
What is 0.0008235 in scientific notation
larisa [96]
I think this is the Answer

8.235*10^-4

7 0
3 years ago
Other questions:
  • I am going to mix a gallon bucket of window cleaner. The instruction direct you mix 1 part cleaner to 3 parts water. How much cl
    15·1 answer
  • The weather forecast states that there’s a 35% chance of rain tomorrow describe a method that you could use to model the situati
    14·1 answer
  • Which statement is true about the end behavior of the graphed function?
    9·2 answers
  • Givenf(x)=8(1-x), what is the value of f(-6)
    12·2 answers
  • Plz help i need need i know the question is really easy but my brain has stopped working
    5·2 answers
  • Help please solve for x<br> i will give brainliest
    6·1 answer
  • For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
    13·1 answer
  • 20.
    8·1 answer
  • If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?
    8·1 answer
  • Solve the absolute value equation or indicate that the equation has no solution. |x-5|=4
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!