Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.
Required:
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
Answer:
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
North Catalina:
Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:
[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]
Chapel Mountain:
Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:
[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
We want that: [tex]N - C > 5[/tex]
Distribution N - C:
The mean is:
[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]
The standard deviation is:
[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 10}{7.3937}[/tex]
[tex]Z = -0.68[/tex]
[tex]Z = -0.68[/tex] has a pvalue of 0.2483
1 - 0.2483 = 0.7517
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
The three most commonly used graphs in research are the histogram, the __________, and the cumulative frequency graph (ogive)
Answer:
The four most common are probably line graphs, bar graphs and histograms, pie charts, and Cartesian graphs.
8) How many terms of the arithmetic sequence (2, 4, 6, 8, ...} will give a sum of 600?
PLZ ANSWER
Answer:
I believe the answer is 300
Step-by-step explanation:
helpppp meet please
Answer:
I think it’s 18
Answer:
18
Step-by-step explanation:
the larger triangle is just a bigger version of the smaller one, and the equal sides show us that it is scaled up to be doubled in size, therefore 9x2=18
a^2 - 2ab^2 if a = 9 and b = 3
I need help please!!
Answer:
3 1/4 + 4 2/5 + 6 1/2 = 14.15 hours
Step-by-step explanation:
m∠1=119∘ and m∠2=61∘.
What is m∠3?
Answer:
m∠3 = 119°
Step-by-step explanation:
All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.
Answer:
K12 answer
Step-by-step explanation:
Write an equation for a line perpendicular to y=4x+1 and passing through the point (12,-7).
y =
Answer:
Step-by-step explanation:
y = 4x + 1
Slope of line = 4
Slope of perpendicular to line = -¼
Point-slope equation for line of slope -¼ that passes through (12, -7):
y+7= -¼(x-12)
Simplify the expression:
P + 7p + 5p
P = ?
A. 13p
B. 13
C. 16p
D. 16
The scatter plot below shows the amount of money Shawn had in the bank on days in the month of January.
Which statement best describes the relationship between the amount of money Shawn had in the bank and the day of the month?
does 7/10 x 80 represent 70% of 80
Answer:
yes
Step-by-step explanation:
MATH 20 POINTS HELP PLZ :)
Answer:
the answer is C.
Step-by-step explanation:
A helicopter hovers 1500 feet above a small island. The
figure shows that the angle of depression from the
helicopter to point P is 40°.
How far off the coast, to the nearest foot, is the island?
400
1500ft
Please help me solve this problem
Answer:
the island is 1787.63ft far.
Step-by-step explanation:
<P=40° alternate angle
in triangle
relationship between perpendicular and base is given by tan angle
tan 40=p/b
tan40=1500/b
b=1500/tan40=1787.63ft
QUESTION 1
1.1
1.1.1 Wiite 2 368 000 in words
1.1.2
Round the following number 864 345,537
1.1.2.1 to the nearest thousand
1.1.2.2 to two decimal places
Why is stock data calculated using the subtraction and addition method instead of a simple moving average? PLEASE HURRY I AM TAKING A TEST
Answer:
The moving average (MA) is a simple technical analysis tool that smooths out price data by creating a constantly updated average price. The average is taken over a specific period of time, like 10 days, 20 minutes, 30 weeks or any time period the trader chooses. There are advantages to using a moving average in your trading, as well as options on what type of moving average to use. Moving average strategies are also popular and can be tailored to any time frame, suiting both long-term investors and short-term traders.
Step-by-step explanation:
One disadvantage to solving systems using substitution is that isolating a variable often involves dealing with messy fractions. There is another method for solving systems of equations: the addition/subtraction method.
In the addition/subtraction method, the two equations in the system are added or subtracted to create a new equation with only one variable. In order for the new equation to have only one variable, the other variable must cancel out. In other words, we must first perform operations on each equation until one term has an equal and opposite coefficient as the corresponding term in the other equation.
sorry it is so long, i hope this helps!
Ellie worked 6 hours on Monday, 4.5 hours on Tuesday, 4 hours on Wednesday, 5.75 hours on Thursday, and 3 hours on Friday. If she is paid $10.18 per hour. Find her gross earnings for the week.
Answer:
⚠️DO NOT RELY ON ME⚠️ But, just by doing It in my head i think it's 236.685, but I don't really know just my thought process and mental math
Find the area of the shaded polygons
Answer:
4 sq un
Step-by-step explanation:
The scale on a map is 1in. = 2 mi. On the map, Greg’s house is 4in. from Melissa’s house. What is the actual distance from Greg’s house to Melissa’s house?
The distance from Greg's house to Melissa's is 8 mi.
Step-by-step explanation:
Multiply 4 by 2.
What value of y makes the equation 3y+ 9 = 36 true?
Answer:
y=9
Step-by-step explanation:
Confusing to me please help......
Hi there!
[tex]\large\boxed{3 \text{ boxes}}[/tex]
Calculate the number of boxes of cubes needed by calculating the volume of the pictured figure.
We can see that it has a width of 4 blocks, depth of 2 blocks, and a height of 8 blocks.
Calculate volume: V = l × w × h
V = 4 × 2 × 8 = 64 cubes in each box.
Since she needs 140 cubes, we can find how many boxes she would need for this amount:
140 ÷ 64 = 2.1875.
However, you cannot buy a part of a box, which is why you must round to a whole number. However, only buying 2 boxes would be too little.
Thus, she would need to buy 3 boxes.
y∝1√x
If
y=7 when x=64
find,
x when y=8
Answer:
uhm im really sorry about this but i really need points i would help but id get it wrong im bad aat math
Step-by-step explanation:
Which statement correctly compares the spreads of the distribution
Answer:
From what I remember A is the answer but im not sure.
Answer:b
Step-by-step explanation:t
Quadrilateral ABCD is a parallelogram with < BCA= 50 , < DCA=60, find value of
Answer:
[tex]ADC = 70[/tex]
Step-by-step explanation:
Given
[tex]BCA = 50[/tex]
[tex]DCA = 60[/tex]
See attachment for parallelogram and complete question
Required
Find ADC
From the attachment:
[tex]BCD = BCA + DCA[/tex]
[tex]BCD = 50+60[/tex]
[tex]BCD = 110[/tex]
Adjacent angles add up to 180.
So:
[tex]ADC + BCD = 180[/tex]
[tex]ADC = 180-BCD[/tex]
[tex]ADC = 180-110[/tex]
[tex]ADC = 70[/tex]
How many more people studied for 0-30 minutes than people who studied for 121-150 minutes?
Answer:
5 more people studied more in 0-30 minutes than people who studied 121-120 minutes.
Step-by-step explanation:
x over 8 = 10?
i just need to solve for x
is -1 equivalent to -3 - (-12)
Answer:
no
Step-by-step explanation:
-1 - (-12)
the two negative signs before the 12 cancel out so it ends up being
-1+12
-1+12=11
11 and -1 are not equal to each other
Answer:
No
Step-by-step explanation:
-3-(-12)=-3+12
-3+12=9
Please Help!!! I'll Give Best And Brainliest if it lets me!
Answer:
6
Step-by-step explanation:
this is the answer. have a great day.
If you leave $2300 in an account earning 3% interest, compounded daily, how much money will be in the account after 5 years? (Round your answer to two decimal places.)
Answer:
$2672.20
Step-by-step explanation:
2300(1+(0.03)/(365))^(5*365)
=$2672.20
Choose all that apply!! i’ll give a brainly!!
Step-by-step explanation:
The answer is A
PLEASE FOLLOW ME
18(3x+1)+3 ; x=2 evaluate the expression for the given value of the variable.
Answer:
Not sure but I think the answer is 129
Step-by-step explanation:
first, substitute the value of x in the expression like this
18(3*2+1)+3
after substituting, our work has made easier
18(6+1)+3
18(7)+3 or simply 18*7+3
126+3
129