Answer:
a) 0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b) 369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c) Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A result is considered significantly high if it is more than 2.5 standard deviations above the mean.
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that 24.5% of people have sleepwalked.
This means that [tex]p = 0.245[/tex]
Sample of 1478 adults:
This means that [tex]n = 1478[/tex]
Mean and standard deviation:
[tex]\mu = 1478*0.245 = 362.11[/tex]
[tex]\sigma = \sqrt{1478*0.245*0.755} = 16.5346[/tex]
a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.
Using continuity correction, this is [tex]P(X \geq 369 - 0.5) = P(X \geq 368.5)[/tex], which is 1 subtracted by the p-value of Z when X = 368.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{368.5 - 362.11}{16.5346}[/tex]
[tex]Z = 0.39[/tex]
[tex]Z = 0.39[/tex] has a p-value of 0.6517
1 - 0.6517 = 0.3483
0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b. Is that result of 369 or more significantly high?
362.11 + 2.5*16.5346 = 403.4
369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c. What does the result suggest about the rate of 24.5%?
Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
Please help!!!
Select the correct answer
Does anyone know how to do probability good?
Answer:
Yes, I can help you for free if you help me on some of my questions
Step-by-step explanation:
What is the area of the parallelogram?
20 cm 2
40 cm 2
20 cm 2
40 cm 2
What is 5/2(4x+8) in simplified form?
13/2x+8
10x + 20
13/2x+21/2
10x + 8
got u
Step-by-step explanation:
the answer is 10x+20
Lisa buys 3 pints of milk how many cups did Lisa buy?
Answer:
3 pints = 6 cups
Step-by-step explanation:
Formula: multiply the volume value by 2
Answer:
6 cups
Step-by-step explanation:
1 pint = 2 cups
3 pints = 3x2 cups
3 pints = 6 cups
If this helps please mark as brainliest
Lines AB and CD are perpendicular to each other. If 3 measures (4x + 4)°, and 4 measures 26°, what is the value of x?
Please justify your answer, I really don't understand it.
9514 1404 393
Answer:
A x = 15
Step-by-step explanation:
Lines AB and CD being perpendicular means the angles where they meet are all 90°. The diagonal line divides two of those 90° angles into two parts (each). The whole (90°) is the sum of the parts into which the angle has been divided.
The sum of angles 3 and 4 is 90°. Once you understand this relationship, you can write an equation based on the relationship. The equation can be solved in the usual way.
(4x +4)° +26° = 90°
4x = 60 . . . . . . . . . . . . divide by °, subtract 30
x = 15 . . . . . . . . . . divide by 4
The hungry caterpillar was 5.4 feet away from his favorite leafy bush. He crawled 1.2 feet every hour to reach the leaves. How many hours did it take him to reach the bush?
Answer:
About 4.5 hours
Step-by-step explanation:
STREAM ANCIENT DREAMS IN A MODERN LAND FOR BRAINLIEST
What is 1.05 x 10^8 written in standard notation?
Answer:
105000000
Step-by-step explanation:
Since the exponent of the scientific notation is positive, move the decimal point 8 places to the right.
After writing the expression in standard form we get 105000000
What are exponents ?
An exponent is a number or letter written above and to the right of a mathematical expression called the base. It indicates that the base is to be raised to a certain power.
The given question is 1.05 * 10⁸
It has to be written in the standard format
The exponent 8 on 10 means base 10 is multiplied 8 times.
therefore
1.05 * 10*10*10*10*10*10*10*10
On solving this we get
105000000 is what we get after writing the expression in standard form.
To know more about Exponent
https://brainly.com/question/5497425
#SPJ2
Which point is graphed on the coordinate plane? у 10 5 4 3 2 ہے X 0 1 2 3 4 5 6 7 8 9 10 (3,8) (8,8) (3,3) (8,3)
Answer: (3, 8)
Hope it helps :)
The point graphed on the coordinate plane is either (3,8) or (8,8), depending on whether the horizontal axis is labeled from left to right or right to left.
What is graph?A graph is a visual representation of data or a mathematical equation. It is used to show the relationship between two or more variables, usually depicted on the horizontal and vertical axes of the graph.
The given points are of the form (x,y), where x is the horizontal axis coordinate (also known as the x-axis) and y is the vertical axis coordinate (also called the y-axis).
Each point in the given options is represented by its (x,y) coordinates. Based on the options provided, we must determine which point is graphed on the coordinate plane.
So, to accomplish this, we simply compare the (x,y) coordinates of each option to the coordinates on the graph and select the option that matches.
Thus, (3,8) or (8,8) can be the coordinate plane.
For more details regarding graph, visit:
https://brainly.com/question/17267403
#SPJ7
how did u arrive at the answer?
People who experience online harassment either ignore it or respond via postings or involving authorities Is one method more effective than the other? A 2014 Pew Research Center report, based on a random sample of American adults, found that 412 of the 549 respondents who had chosen to ignore online harassment thought that it was an effective way to deal with the issue. Of the 368 respondents who had chosen to respond to online harassment, 305 thought that it had been effective A.
Required:
a. Is there good evidence that one approach is more likely to be effective than the other? State the null and alternative hypotheses, obtain the test statistic and P-value, and conclude in context.
b. How large is the difference? Obtain and interpret in context a 95% confidence interval for the difference between the proportions of American adults who find ignoring online harassment effective and those who find responding to it effective.
c. How effective is that best method? Obtain and interpret in context a 95% confidence interval for theproportion of American adults who find the best m ethod effective.
Answer:
Step-by-step explanation:
First method information:
Sample size n₁ = 549
x₁ ( people ignoring on-line harassment ) = 412
Proportion of people ignoring on-line harassment p₁
p₁ = 412/549 p₁ = 0,75 q₁ = 1 - p₁ q₁ = 0,25
Second method ( people chosen to respond)
Sample size n₂ = 368
number of people responding x₂ = 305
Proportion of people responding
p₂ = 305/ 368 p₂ = 0,83 then q₂ = 0,17
a) Looking for differences in the approachs
Hypothesis test:
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
Alternative Hypothesis indicates that the test is a two-tail test
Choosing a confidence interval CI = 95 % then a significance level is α = 5% α = 0,05 and from z-table we get z(c) = 1.64
To calculate z(s)
z(s) = ( p₁ - p₂ ) / EED
EED = √ p₁*q₁)/n₁ + (p₂*q₂)n₂
EED = √ (0,75*0,25)/549 + 0,83*0,17)/368
EED = √ 3,41 *10⁻⁴ + 3,83*10⁻⁴
EED = 10⁻² *√ 3,41 + 3,83
EED = 10⁻² * 2,69
EED = 0,0269
z(s) = ( p₁ - p₂ )/0,0269
z(s) = - 0,08 / 0,0269
z(s) = - 2,97
p-value for z(s) is pvalue = 0,0015
Comparing z(s) and z(c) modules
z(s) > z(c) therefor z(s) is in the rejection region we have to reject H₀ and claim that there is a difference between the proportions
b) How large is the difference
Avery spent 170 minutes outside. If
she spent 64 minutes riding her bike,
48 minutes on the trampoline, and the
rest of the time swimming, how many
minutes did Avery spend swimming?
Answer:
58 minutes
Step-by-step explanation:
s = 170 - 64 - 48
s = 58
Answer:
Avery spent 58 minutes swimming
Step-by-step explanation:
Simplify.
Help me please
Answer:
answer is 3^2
hopefully this helps someway
Collette wanted to know if there was a difference in favorite food types among students at her large high school. She took a random sample of students from her school and asked them to name their favorite food type. Of those surveyed, 29 preferred American, 16 preferred Chinese, 19 preferred Mexican, and 28 preferred Italian. Which of the following is the chi-square test statistic?
a. (29 - 23)2/23 + (16 - 23)2/23 + (19 - 23)2/23 + (28-23)2/23.
b. (29 - 23)2/23 - (16 - 23)2/23 - (19 - 23)2/23 - (28 - 23)2/23.
c. (29 + 23)2/23 + (16 + 23)2/23 + (19 + 23)2/23 + (28+23)2/23.
d. (29 - 23)2/92 + (16 - 23)2/92 + (19 - 23)2/92 (28-23)2/92.
e. (29 + 23)2/92 + (16 + 23)2/92 + (19 - 23)2/92 + (28-23)2/92.
Answer:
(29-23)²/23 + (16-23)²/23 + (19-23)²/23 + (28-23)²/23
Step-by-step explanation:
Given :
n(American) = 29
n(Chinese) = 16
n(Mexican) = 19
n(Italian) = 28
Expected value = (29 + 16 + 19 + 28) / 4
Where, 4 = sample size
Expected value, E = 23
χ² = (Observed value - Expected value)² / expected value
χ² = (29-23)²/23 + (16-23)²/23 + (19-23)²/23 + (28-23)²/23
Answer:
(29-23)²/23 + (16-23)²/23 + (19-23)²/23 + (28-23)²/23
Step-by-step explanation:
I would but you probobly want just the answer :/
what is the area of this figure
Answer:
Hello! answer: 10
Step-by-step explanation:
Formula for area of squares: base × height
Formula for area of triangles: base × height ÷ 2
2 × 2 = 4
2 × 2 ÷ 2 = 2
4 × 2 ÷ 2 = 4
4 + 2 + 4 = 10 therefore the area is 10 hope that helps!
The sequence of the differences, 2, 4, 8, 16, 32, … is a geometric sequence with:
a1 =
and r1 =
*Please Help**
Answer:
r1 is given by the formula an=a1r.n-1
Step-by-step explanation:
Answer:
a1 = 2
r1 = 2
yayyyyyyyyyyyyyyyyyyyyyyyyy
in the number 78.9 what digit is in the tenths places
Answer:
9
Step-by-step explanation:
Plz help me well mark brainliest!!
Answer:
It's B
Step-by-step explanation:
A recipe book has 24 appetizer recipes
and 37 dessert recipes. There are 10
more dinner recipes as appetizer and
dessert recipes combined. How many
recipes are in the book in all?
Find the slope of the line that passes through these points.
(7,3), (-5,3)
Answer:
0
Step-by-step explanation:
=> m = 3 -3/7+5
=> m = 0/12
=> m = 0
The Consumer Reports National Research Center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,740 of the respondents think the future health of Social Security is a major economic concern.
Required:
a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern.
b. At 90% confidence, what is the margin of error?
c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern.
d. Develop a 95% confidence interval for this population proportion.
Answer:
a. 0.87
b. The margin of error is of 0.0124.
c. The 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is (0.8576, 0.8824).
d. The 95% confidence interval for this population proportion is (0.8553, 0.8847).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence interval is:
[tex]\pi \pm M[/tex]
a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern.
The sample proportion, that is, 1740 out of n = 2000. So
[tex]\pi = \frac{1740}{2000} = 0.87[/tex]
0.87 is the point estimate.
b. At 90% confidence, what is the margin of error?
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Then the margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.87*0.13}{2000}}[/tex]
[tex]M = 0.0124[/tex]
The margin of error is of 0.0124.
c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern
[tex]\pi - M = 0.87 - 0.0124 = 0.8576[/tex]
[tex]\pi + M = 0.87 + 0.0124 = 0.8824[/tex]
The 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is (0.8576, 0.8824).
d.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Then the margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.87*0.13}{2000}}[/tex]
[tex]M = 0.0147[/tex]
The confidence interval will be of:
[tex]\pi - M = 0.87 - 0.0147 = 0.8553[/tex]
[tex]\pi + M = 0.87 + 0.0147 = 0.8847[/tex]
The 95% confidence interval for this population proportion is (0.8553, 0.8847).
Please someone help me on this :c
Scientific notation questions
Best answer gets Brainliest and 20 points
(All of the questions are on the picture)
Please answer this ASAP
*NO LINKS OR QUESTION REPORTED*
[tex]1. \sf{\ Given : \bigg(\dfrac{10^5}{10^2}\bigg) (10^2)^3}[/tex]
The above expression can be written as :
[tex]\implies \sf{10^{(5-2)}}.10^{(2)(3)}}[/tex]
[tex]\implies \sf{10^{(3)}}.10^{(6)}}[/tex]
As Bases are same, we can add the powers with same base
[tex]\implies \sf{10^{(3 + 6)}}}}[/tex]
[tex]\implies \sf{10^{9}}}}[/tex]
[tex]2. \sf{\ Given : \dfrac{10^5}{10^3.10^8}}[/tex]
The above expression can be written as :
[tex]\implies\sf{\dfrac{10^5}{10^{(3 + 8)}}}[/tex]
[tex]\implies\sf{\dfrac{10^5}{10^{11}}}[/tex]
[tex]\implies\sf{10^{(5 - 11)}}[/tex]
[tex]\implies\sf{10^{-6}}[/tex]
[tex]3. \sf{\ Given : \dfrac{10^{-2}.10^{-3}}{(10^2)^{-5}}}[/tex]
[tex]\implies\sf{\dfrac{10^{(-2 - 3)}}{10^{(2)(-5)}}}[/tex]
[tex]\implies\sf{\dfrac{10^{(-5)}}{10^{(-10)}}}[/tex]
[tex]\implies\sf{10^{(-5 + 10)}}[/tex]
[tex]\implies\sf{10^{5}}[/tex]
[tex]4. \sf{\ Given : (2.5\ x \ 10^8)(8\ x \ 10^3)[/tex]
[tex]\implies \sf{(2.5 \ x \ 8)(10^{(8 + 3)})}[/tex]
[tex]\implies \sf{(20)(10^{11})}[/tex]
[tex]\implies \sf{2 \ x \ 10^{12}}[/tex]
[tex]5. \sf{\ Given : \dfrac{27.8 \ x \ 10^{8}}{25 \ x \ 10^{3}}}[/tex]
[tex]\implies\sf{1.112\ x \ 10^{(8 - 3)}}[/tex]
[tex]\implies\sf{1.112\ x \ 10^{5}}[/tex]
Find BD if AC = 47 yards
9514 1404 393
Answer:
21 yards
Step-by-step explanation:
The area of a quadrilateral with diagonals that are right angles to each other is given by ...
A = (d1)(d2)/2 . . . . where d1 and d2 are the lengths of the diagonals
493.5 yd² = (47 yd)(BD)/2 . . . . . . . . . . fill in the given information
Dividing by the coefficient of BD, we have ...
(2)(493.5 yd²)/(47 yd) = BD = 21 yd
This is not a question but an answer for those out there who need it. I know I really needed this, so I hope you will find it helpful too.
) He fills the pencil holder with sand before he wraps it to make it feel like a heavy, expensive gift. How much sand will he need to "borrow" from his sister's sandbox to fill the pencil holder? *
ANSWER:
1/2 * 3 = 1.5
1.5*2=3
3*3.5=10.5
ANSWER = 10.5
Answer:
im confused q or a??
Step-by-step explanation:
6 Gallons and 3 quarts = ________ quarts?
Answer: is 27 quarts
Step-by-step explanation:
Answer: 27 quarts
Step-by-step explanation:
6 gallons is 24 quarts. Add the 3 to get 27. Formula: Gx4= Q
6x4=24 Plus the 3 extra= 27 quarts Hope this Helps uwu
Pn.
2. A handkerchief measures 22 cm long and 20 cm wide. Jenny wants
to put a lace around it. How many centimeters of lace will she buy to
decorate its sides?
A- What is asked?
G-What are the given facts?
O-What operation to be use?
N- What is the number sentence?
S- How do you solve the number sentence?
A-What is the answer?
Answer:
Français is a new digital currency developed by Stanford PhDs and the other is the first team accept a girl for playing with the bear who heart
Answer:
How many centimeters of lace are use to decorate its side of handkerchief.
22 cm long, 20 cm wide
Multiplication
22 x 20 = N
22 cm x 20 cm = 440 square centimeters
440 square cm
What type of quadrilateral is DEFG? Select all that apply.
ty
F
E
6
2
G
2
D
o
2
A rhombus
B. parallelogram
C! square
DE
D trapezoid
Answer:
B. parallelogram
Step-by-step explanation:
Given
See attachment for quadrilateral
Required
Select the type of quadrilateral
From the attached image, we have:
[tex]DE = FG[/tex] -- Opposite, Parallel and Equal
[tex]EF = GD[/tex] -- Opposite, Parallel and Equal
Since all 4 sides are not equal, then it is neither a square; nor a rhombus
Hence, the shape is a parallelogram
CAN SOMEONE HELP ME!
Answer:
26
Step-by-step explanation:
5 × 4 = 20 (rectangle)
8-5 = 3 (triangle)
3×4÷2 = 6
20+6 = 26
The mayor of a large city will run for governor if he believes that more than 30 percent of the voters in the state already support him. He will have a survey firm ask a random sample of n voters whether or not they support him. He will use a large sample test for proportions to test the null hypothesis that the proportion of all voters who support him is 30 percent or less against the alternative that the percentage is higher than 30 percent. Suppose that 35 percent of all voters in the state actually support him. In which of the following situations would the power for this test be highest?
a. The mayor uses a significance level of 0.01 and n = 250 voters.
b. The mayor uses a significance level of 0.01 and n = 500 voters.
c. The mayor uses a significance level of 0.01 and n = 1,000 voters.
d. The mayor uses a significance level of 0.05 and n = 500 voters.
e. The mayor uses a significance level of 0.05 and n = 1,000 voters.
Answer:
e. The mayor uses a significance level of 0.05 and n = 1,000 voters.
Step-by-step explanation:
Power of a test:
For a high power of a test, two conditions are needed:
Large significance level.
Large sample.
In this question:
A significance level of 0.05 will lead to a higher power than a significance level of 0.01, which means that the answer is between options d and e.
A test with a sample of 1000 has a higher power than a test with a sample of 500, and thus, the answer is given by option e.