Scores of an IQ test have a bell-shaped distribution with a mean of and a standard deviation of . Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between and ? (b) What percentage of people has an IQ score less than or greater than ? (c) What percentage of people has an IQ score greater than ?
Complete question is;
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?
Answer:
A) 68% of the people had an IQ score between 87 and 113
B) 5% of the people had IQ scores less than 74 and greater than 126.
C) 0.15% had an IQ score greater than 139
Step-by-step explanation:
We are given;
Mean; x¯ = 100
Standard deviation; σ = 13
According to the empirical rule in statistics;
>> 68% of the data lies within one standard deviation of the mean
>> 95% of the data lies within two standard deviations of the mean
>> 99.7% of the data lies within three standard deviations
A) We want to find the percentage of people with an IQ score between 87 and 113.
Within one standard deviation, we have;
x¯ ± σ
>> (100 - 13), (100 + 13)
>> (87, 113) which is the range we are looking for.
Thus, 68% of the people had an IQ score between 87 and 113
B) we want to find percentage of people has an IQ score less than 74 or greater than 126.
Let's first find those who had between 74 and 126.
Let's use two standard deviations within the mean.
x¯ ± 2σ
>> (100 - (2×13)), (100 + (2×13))
>> (74, 126) which is the range we are looking for.
So percentage that have IQ scores between 74 and 126 is 95%
Thus;
Percentage of those who had less than 74 and greater than 126 is;
P = 1 - 95%
P = 5%
C) we want to find the percentage of people that had an IQ score greater than 139.
Let's use the z-score formula;
z = (x¯ - μ)/σ
z = (139 - 100)/13
z = 39/13
z = 3
This means it is 3 standard deviations above the mean.
Thus;
Since it's one side outside the mean, then;
Percentage of people with an IQ score greater than 139 = (1 - 99.7%)/2 = 0.3%/2 = 0.15%
Can somebody help me? I need help ;-;...
Answer:
Bottom left
Step-by-step explanation:
Dots are on the inside and outside of the line as well as being on the line
If an object is projected upward with an initial velocity of 125 ft per sec, its height h after t seconds is h= - 16t+ 125t. Find the height of the object after 2 seconds.
Answer:
h(t) = -16t^2+125t
We need to find h(t) when t = 4 s:
h(4) = -16*4^2+125*4
h(4) = 244 ft
The height of the object after 4 seconds is 244 feet.
What is the acceleration of a 4.5 kg mass when there is a net force of 18 N on
it? Please show me the equation if you know.
Answer:
Step-by-step explanation:
a=F/m
a=18/4.5
a=4 m/s/s
hope this helped! :D
which is a true statement about 10 days of production
Answer:
At 10 days, no line is above the '0' means no one is producing widgets at 10 days point. Since the y axis represents number of widgets produced, this means none of the plants have produced more than 0 widgets yet.
Which equation represents a circle that has a center at and a radius of 5?
what are the options?
Expand (2+x)^3 using binomial theorem
Step-by-step explanation:
= 2³ + x ³ + 3(2)²x + 3(2)x²
= 8 + x³ + 12x + 6x²
= x³ + 6 x² + 12 x + 8
Select the correct answer.
Which function is the inverse of f(x) = -x^3 - 9?
Answer:
(2)
Step-by-step explanation:
Let f(x) = y → f-¹(x) = f(y) = x, f(y) is the inverse of f(x)
Thus,
=> -x³ - 9 = y
=> - y - 9 = x³
=> (-y - 9)^(1/3) = x
=> f(y) = x
Inverse is (-y-9)^(1/3)
Replacing the variable, inverse is (-x-9)^(1/3)
Option (2)
need help geometry question central angles and arcs !!! PLS HELP
Answer:
150°
Step-by-step explanation:
35 + 120 + 55 = 210
360 - 210 = 150
Semira’s puppy weighs 12.4 pounds and is growing at a rate of 0.8 pound per week. Cedric’s puppy weighs 9.2 pounds and is growing at a rate of 1.2 pounds per week. Let x represent the time in weeks and y represent the weight of the puppy in pounds. Which system of equations can Semira and Cedric use to determine after how many weeks their puppies will weigh the same?
{y=0.8x+12.4
{y=1.2x+9.2
{y=12.4x+0.8
{y=9.2x+1.2
{y=0.8x+1.2
{y=12.4x+9.2
{y=1.2x+0.8
{y=9.2x+12.4
what is 10(x-2)-(x-4)
What value of a satisfies the following equation?
-2(a + 3) = -4a + 32
Answer:
a = 19
Step-by-step explanation:
-2(a + 3) = -4a + 32
-2a - 6 = -4a +32
+2a +2a
-6 = -2a + 32
-32 -32
-38 = -2a
divide by -2
a = 19
Answer:
a=19
Step-by-step explanation:
-2(a+3) = -4a + 32
-2a - 6 = -4a + 32(Group like terms)
-2a+4a=32+6
2a=38(Divide both sides by 2)
a=19
HELP PLEASE DO NOT PUT A LINK
Answer:
No
No
Yes
Yes
No
Step-by-step explanation:
HELP PLS!! according to the rational root theorem, -2/5 is a potential rational root of which function?
Answer:
hi
Step-by-step explanation:
According to the Rational Roots Theorem, the possible rational roots are all the factors of the constant term expressed over the factors of the leading coefficient of the polynomial function. The reason is that the numerator of this rational root is a factor of 4 and the denominator is a factor of 25.
DOES IT HELP?!
Answer: D
Step-by-step explanation: Got it right
How do you find out if a number is an integer or not?
Answer:
Integers are any whole number negative or positive
Step-by-step explanation:
Please help me.
1. Reflect triangle PQR over the y-axis. Then, describe what happened to each of the coordinates.
2. Reflect your new triangle P’Q’R over the x-axis. Describe what happened to each of the coordinates
Answer:
make dot in the 2,2 8,2 and 5,7 and join the dots
Together, Dien and Jane can eat 2/3 of a pizza in 4 seconds. How long would it take each of them to eat the whole pizza alone if Jane can eat a pizza 5 seconds faster than Dien?
Answer:
Dien - 15 seconds, Jane - 10 secondsStep-by-step explanation:
Together:
2/3 of pizza ⇒ 4 secondsFull pizza ⇒ 4 ÷ 2/3 = 6 secondsDien needs x seconds to eat pizza
Jane needs x - 5 seconds to eat pizza
In one second, Dien can eat 1/x, Jane can eat 1/(x - 5), together 1/6 of a pizza
1/x + 1/(x - 5) = 1/6x(x - 5) = 6(x + x - 5)x² - 5x - 12x + 30 = 0x² - 17x + 30 = 0(x - 15)(x - 2) = 0x = 15 (x = 2 is discounted as not realistic)Dien can eat a pizza in 15 seconds, Jane can eat a pizza in 10 seconds
jim began to bike a 173 mile bicycle trip to build up stamina for a for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours. If Jim walks at a rate of 4 miles per hour and rides at the rate of 38 miles per hour , find the amount of time he spent on the bicycle
Answer
3.5 hours
Step-by-step explanation:
Let us represent
The time spent walking as x
The time spent riding as y
Jim began a 146-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours.
Hence:
x + y = 5.... Equation 1
x = 5 - y
If Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour,
The formula for Distance = Speed × time. Hence,
4 × x + 40 × y = 146 miles
4x + 40y = 146.... Equation 2
We substitute 5 - y for x in Equation 2
4(5 - y) + 40y = 146
20 - 4y + 40y = 146
Subtract 20 from both sides
20 - 20 - 4y + 40y = 146 - 20
- 4y + 40y = 146 - 20
36y = 126
y = 126/36
y = 3.5 hours
Since the time he spent raiding his bicycle is represented by "y", the amount of time he spent on the bicycle is 3.5 hours
I think this is right I had this question I think it was the same one I dont know tho
I need help what the value of x and adjacent or vertical?
Answer:
74 degrees
The angles are adjacent, since they have a common side (adjacent basically means right next to each other).
Step-by-step explanation:
180 - 106 = 74
Both angles are supplementary, since they add up to 180 (make a straight line together).
In the linear equation y = 4x + 2, the value 2 represents which of the following?
A:The slope of the line
B: The y- coordinate of the y-intercept
C: The x-coordinate of the y-intercept
D: The quadrant in which the line lies
I want a expert or someone that can tell me this %100 I’m offering a brainalist + 20 points
Answer:
The answer is A
Step-by-step explanation:
Supplementary angles are angles which add up to 180°
∠1 and ∠3 add up to 180°, so they are supplementary.
The final task is a bit more difficult. The bookshelf consists of two cubes and each cube has a side of (1/2). This is a fractional base, so the expression for both cubes looks like this: (1/2)^3 x 2. Calculate the volume of the bookshelf to complete your training!
Answer:
1/4
Step-by-step explanation:
I think that the expression is correct
(1/2)^3 x 2 = 1/8 x 2 = 1/4
Determine whether the situation calls for a survey, an observational study, or an experiment. You want to find out if a new drug can help decrease the symptoms of migraine headaches.
experiment
observational study
survey
observational study is the wrong answer
Answer:
Experiment.
Step-by-step explanation:
It helps you determine the effect of the medication in a controlled environment with variables and controls.
Find the Surface Area. I need the answer fast.
Answer:
1615
Step-by-step explanation:
Area of triangle is: A= B•H•1/2
Area of square is A= L•W
39•17•1/2= 331.5
331.5•4= 1326
17•17= 289
Add the square area to the area of the triangles
289+ 1326= 1615
hope this helps chu <3
Answer:
663
Step-by-step explanation:
Since we are finding the area we multiply Length times Width which is a way of finding formal. L x W so the Length is 17 and Width is 39 so
17 x 39 = 663. So the area is 663
you invested money in two funds. last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you receive a total of $921. This year, the first fund paid a 10% dividend and the second only 1%, and you received a total of $846. How much money did you invest in each fund?
Answer:
x= $ 7100 investment in first fund
10x+y=84600 substitute the value of x
10*7100+y=84600
y=84600-71000
y= $ 13600 investment in second fund.
Step-by-step explanation:
Math help!
Please only answer if you know the answer, the comment section is right below. Please don't waste my points!
Also, please show all of your work, you are trying to help me better understand the concept, not just give me the answer.
The image is down below. Show work! Thanks!
Answer: 1675 Ft. = Distance from
fire to the windmill.
Step-by-step explanation:
tan8 = 140/X1.
X1 = 140/tan8 = 996.2 Ft.
tan3 = 140/(996+X2)
996+X2 = 140/tan3 = 2671
X2 = 2671-996 = 1675 Ft. = Distance from
fire to windmill.
You invest $2,000 in an investment that pays an annual interest rate of 7.5% with monthly compounding. How many months will it take for your investment to be worth $3,500
Answer:
10 years
step-by-step explanation:
First, divide 7.5 by 100, you should get 0.075, then multiply 0.075 by 2000, you should get 150, thats how much interest he gains each year, now subtract 2000 from 3500 to see how much he needs to get to 3500, you should get 1500, now divide 1500 by 150, you should get 10, which is how many years he will need to get to 3500 from 2000
what is the value of x?
Step-by-step explanation:
Continuation of the answer
4x=180 degrees
X=180/4=45 degrees.
Use the Distributive Property to solve the equation.
- 3(x + 2) = 18
If you solve you get 50 points so pls help and no links pls
Answer:
x = -8
Step-by-step explanation:
-3x -6 = 18
-3x = 24
x = -8
HELP ME I BEED THIS DONE!