Answer:
Step-by-step explanation:
4/4
8/6
4/6
Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of an answer to a question is independent of the correctness of answers to other questions. Jodi is a good student for whom p = 0.81.
Required:
a. Use the Normal approximation to find the probability that Jodi scores 77% or lower on a 100-question test.
b. If the test contains 250 questions, what is the probability that Jodi will score 77% or lower?
c. How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
d. Laura is a weaker student for whom p = 0.76. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?
Answer:
a) 0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.
b) 0.9463 = 94.63% probability that Jodi will score 77% or lower.
c) 400 questions.
d) Yes, because the formula is the same, independently of the value of p.
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.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.81[/tex]
Question a:
100 questions means that [tex]n = 100[/tex]
For the approximation, we have that:
[tex]\mu = p = 0.81[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]
This probability is the pvalue of Z when X = 0.77. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.77 - 0.81}{0.0392}[/tex]
[tex]Z = 1.02[/tex]
[tex]Z = 1.02[/tex] has a pvalue of 0.8461
0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.
Question b:
Now [tex]n = 250[/tex], so:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{250}} = 0.0248[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.77 - 0.81}{0.0248}[/tex]
[tex]Z = 1.61[/tex]
[tex]Z = 1.61[/tex] has a pvalue of 0.9463
0.9463 = 94.63% probability that Jodi will score 77% or lower.
Question c:
The formula for the standard deviation is:
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Meaning that it is inversely proportional to the square root of the sample size.
So, to reduce the standard deviation by half, the number of question must be multiplied by (2)^2 = 4.
100*4 = 400
So 400 questions.
d. Laura is a weaker student for whom p = 0.76. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?
Yes, because the formula is the same, independently of the value of p.
Which table represents the statement "A car is traveling at a rate of 60 miles per hour"?
Answer:
B
Step-by-step explanation:
because if the car is traveling at 60 mph, the distance traveled would be 60 x the number of hours
Answer:
b
Step-by-step explanation:
I took the exam hopes this helps
If you add 3 groups of 10 to 100, what is the total? How do you know?
Answer:
130
Step-by-step explanation:
3*10 =30+100=130
What is the area of this
Answer:
24
Step-by-step explanation:
Its just 1/2 6x8=24.
its like 6x8=48 and half of it is 24
Choose the expression that best represents the phrase below.
... the product of the width and the height...
A. Wh
B. w-h
C. W + h
D. h w
E. W:h
F. h-w
Answer:
option E is your correct answer
mark as brainliest
PLEASE HELP FAST I WILL GIVE YOU 25 POINT
Answer:
The answer is D
Step-by-step explanation:
Since there are a total of 30 chips and 10 yellow ones, you have to divide then convert them into a fraction.
10/30 = 1/3
AABC maps the outline of a new park. What is the area of the park?
Answer:
C. 10
Step-by-step explanation:
AC = 4 units
BC = 5 units
use the triangle formula
1/2 × 4 × 5 = 10
what is 81 divided by 9
Answer:
9
Step-by-step explanation:
9
9x9 = 81
Therefore, 81 ÷ 9 is 9
solve the rational equation 8-6/x=5+12/x
Answer:
X = 6
Step-by-step explanation:
what is the unknown number in sequence 2
In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each point using values of rr such that r≥0 and values of θ such that 0≤θ<2π. Visually check your answers to ensure they make sense.
(x,y)=(2,5) corresponds to (r,θ)=
(x,y)=(−3,3) corresponds to (r,θ)=
(x,y)=(−5,−3.5) corresponds to (r,θ)=
(x,y)=(0,−5.4)corresponds to (r,θ)=
Step-by-step explanation:
We have cartisean points. We are trying to find polar points.
We can find r by applying the pythagorean theorem to the x value and y values.
[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]
And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.
[tex] \tan(x) = \frac{y}{x} [/tex]
Remeber since we are trying to find the angle measure, use inverse tan function
[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]
Answers For 2,5
[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]
So r=sqr root of 29
[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]
So the answer is (sqr root of 29,68).
For -3,3
[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]
[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]
Use the identity
[tex] \tan(x) = \tan(x + \pi) [/tex]
So that means
[tex] \tan(x) = 135[/tex]
So our points are
(3 times sqr root of 2, 135)
For 5,-3.5
[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]
[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]
So our points are (sqr root of 37.25, 35)
For (0,-5.4)
[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]
So r=5.4
[tex] \tan {}^{ - 1} (0) = undefined[/tex]
So our points are (5.4, undefined)
An airplane is flying 4 miles directly over your house. The distance between your house and the airport is 12 miles. How far apart are the airplane and the airport?
Answer:
c=7.180 miles. 2. Jack is on one side of a 200-foot-wide canyon and Jill is on the other. Jack and Jill can both ... a=2.947 miles. 5. Airplane A is flying directly toward the airport which is 20 miles away. The pilot notices ...
Calculate the volume of a square-based pyramid with a slant height of 5 ft and base edges of 6 ft.
Answer:
Volume is 60ft³
Step-by-step explanation:
b²h/3
b=6
h=5
The volume of a square-based pyramid will be 180 ft³. Option D is correct.
How to find the volume of a prism?If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is the same as its base, then its volume is:
[tex]\rm V = B^2 \times h \\\ V = 6^2 ft \times 5 \ ft \\\ V=180 \ ft^2[/tex]
Learn more about the volume of a prism refer:
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The length of a park bench is 1.5 meters. What is the length of the bench in millimeters?
Answer:
1500 millimeters
Step-by-step explanation:
1 meter = 1000 millimeters
1.5 meters = 1500 millimeters
help me with these 2 pleaseee
Answer:
x=6
Step-by-step explanation:
2x+6=18
2x=12
x=6
Step-by-step explanation:
2(x+3)=18
x+3=18÷2
x+3=9
x=9-3
x=6
2x+15=27-4x
2x+4x=27-15
6x=12
x=12÷6
x=2
Samuel makes a dozen of mini cupcakes using 5/8 cups of sugar, 3 cups of chocolate chips and 1/2 cup of butter. If each cupcake has an equal amount of sugar, how much sugar is used per cupcake?
I don't what form of measurement to use (like grams, cusp, etc.) but I'm pretty sure it'd be cups
I think it's 5/96 or .05208333
So, 5/8 is .625. Dividing that up in throwing it into 12 cupcakes.
Solve for the unknown values.
Answer:
y=45° x=81°
Step-by-step explanation:
the 2 angles across the outside angles sum up to the given number so just subtract 95-50= 45, with that we know subtract from the total sum of every triangle which is 180. So we add the 2 angles we have now, 50+45=99. Now we subtract, 180-99= 81.
Robert bought some plants for his garden. Each plant costs $3.75.
If he spent a total of $52.50, how many plants did he buy?
Show your thinking.
Two buckets of paint each have a mass of 9 kg. If the gravitational force between them is 6.0x10 to the power of minus 10, how far apart are they?
Gravitational force = (gravity x mass1x mass2)/distance^2
6.0x10^-10 = (6.67x10^-11 x 9 x 9)/d^2
D = sqrt(6.0x10^-10/6.67x10^-11 x81)
D = 3.0 m
The answer is B.3.0 m
Answer:
B
Step-by-step explanation:
3.0 m
A pride of lions is growing at a rate of 0.5% per year, compounded continuously. If the growth rate continues, how large will
the pride be after 100 years if it starts with 50 lions. Round your answer to the nearest lion.
Provide your answer below:
Answer:
the answer is 52 Lions
Step-by-step explanation:
I think that's the answer if I'm wrong please tell me if I'm wrongI can ask the people who are around me.
Answer:
82
Step-by-step explanation:
Are all rectangles and squares are parallelograms ?
Answer:
A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Yes, they are.
Answer:
Yes
Step-by-step explanation:
Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.
Hope it is helpful....
Solve 3x2 + 4x + 2 = 0 by using the Quadratic Formula. If necessary, round to the nearest hundredth.
Answer:
Step-by-step explanation:
For this equation: a=3, b=4, c=2
3x2+4x+2=0
Step 1: Use quadratic formula with a=3, b=4, c=2.
x= −b±√b2−4ac / 2a
x= −(4)±√(4)2−4(3)(2) / 2(3)
x= −4±√−8 / 6
Answer:
No real solutions.
The quadratic equation 3x² + 4x + 2 = 0 does not have a real solution.
What are Quadratic Equations?Quadratic equations are second degree polynomial equations which is of the form ax² + bx + c = 0, where a, b and c are integers.
Given quadratic equation is,
3x² + 4x + 2 = 0
Quadratic formula to find the solution is,
x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] / 2a, where [tex]\sqrt{b^2-4ac}[/tex] is called discriminant.
Here, a = 3, b = 4 and c = 2
Substituting,
x = [-4 ± [tex]\sqrt{4^2-(4*3*2)}[/tex]] / (2 × 3)
= [-4 ± √(16 - 24)] / 6
= [-4 ± √(-8)] / 6
This has no real solution since the value inside the discriminant is negative.
Hence the quadratic equation has no real solution.
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IXL question!!!! :geometry-tangent lines
pls help question in the pic
Answer:
Step-by-step explanation:
x-2=24 x=26
PLEASE HELP FAST!!!!!
Answer:
120 feet is the answer
2. The area of the bottom of a shoe box is 28 square inches. If the
height of the shoe box is 3 inches, what is the volume the box
Answer:
Echo stop DELeting MY Stuff
Step-by-step explanation:
Use the table below to answer the following questions.
Answer:
instructions??????????
please help me with the answer u am behind a lot of work trying to avoid 0
Answer:
-3,4
Step-by-step explanation:
just follow up the other coordinates
What is y/x = 8 proportional to?
Answer:
y is directly proportional to 8
while x is inversily proportional to 8
if an inheritance was shared among 72000 to the beneficiaries there were 3 children Ban , Michel and Bob in the ratio of 1:3:4 .how much will each get
Answer:
Ban has 9,000
Michel has 27,000
Bob has 36,000
Step-by-step explanation:
BA: MI: BO
1: 3: 4 (1+3+4 = total number)
BA: [tex]\frac{1}{8}[/tex] of 72,000 (72,000 ÷ 8 x 1) = 9,000
MI: [tex]\frac{3}{8}[/tex] of 72,000 (72,000 ÷ 8 x 3) = 27,000
BO: [tex]\frac{4}{8}[/tex] of 72,000 (72,000 ÷ 8 x 4) = 36,000
Solve each proportion 3/39= y/13
Answer:
[tex]y = 1[/tex]
Step-by-step explanation:
[tex] \frac{3}{39} = \frac{y}{13} [/tex]
Cross multiply
[tex]39 = 39y[/tex]
Divide by 39
[tex]y = 1[/tex]
Answer:
[tex]\boxed {\boxed {\sf y=1}}[/tex]
Step-by-step explanation:
To solve the proportion, we must solve for the variable. This is done by isolating the variable.
[tex]\frac {3}{39}= \frac {y}{13}[/tex]
The variable, y, is being divided by 13. The inverse of division is multiplication. Multiply both sides of the proportion by 13.
[tex]13*\frac {3}{39}= \frac {y}{13}*13[/tex]
[tex]13*\frac {3}{39}=y\\1=y[/tex]
Another way to solve is by cross multiplying. Multiply the 1st numerator by the 2nd denominator, then the 1st denominator and the 2nd numerator.
[tex]\frac {3}{39}= \frac {y}{13}[/tex]
[tex]3*13=39*y\\39=39y[/tex]
Divide both sides by 39 to isolate the variable.
[tex]39/39=39y/39 \\1=y[/tex]
In this proportion, y is equal to 1.