Answer:
The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{3.7}{\sqrt{582}} = 0.3[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 24.1 - 0.3 = 23.8
The upper end of the interval is the sample mean added to M. So it is 24.1 + 0.3 = 24.4.
The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).
Suppose that a category of world-class runners are known to run a marathon in an average of 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons. (Round your answer to two decimal places.)
Answer:
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
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 establishes 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.
Average of 147 minutes with a standard deviation of 12 minutes.
This means that [tex]\mu = 147, \sigma = 12[/tex]
Consider 49 of the races.
This means that [tex]n = 49, s = \frac{12}{\sqrt{49}} = \frac{12}{7} = 1.7143[/tex]
Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons.
This is the p-value of Z when X = 150 subtracted by the p-value of Z when X = 146. So
X = 150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 147}{1.7143}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
X = 146
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{146 - 147}{1.7143}[/tex]
[tex]Z = -0.583[/tex]
[tex]Z = -0.583[/tex] has a p-value of 0.3075.
0.9599 - 0.3075 = 0.6524.
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
a. 1.5
b. 2.3
c. 2.4
d. 1.9
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3
A large soda-pop manufacturer wants to introduce a new design for the label on one of its signature soda-pop drinks. The manufacturer selects a random sample of 150 customers from people who purchase the drink at a large sporting event. Each selected customer is asked whether or not he or she prefers the new design. If the manufacturer were to take a second random sample of 150 customers at the sporting event, the two samples would give somewhat different results in the proportion who prefer the new design. This variation is a source of
Answer:
This variation is a source of
response error.
Step-by-step explanation:
A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.
HELP PLEASE, WILL GIVE BRAINLYIST NOW
Answer:
Step-by-step explanation:
I think you got it correct. The reciprical of this function is y = x.
A)15.8 inches
B) 17.8 inches
C)16.2 inches
D)14.8 inches
Answer:
B
Step-by-step explanation:
Use pythagorean theorem
4^2+5^2=AC^2, AC= 6.4
7^2+9^2=CB^2, CB=11.4
The ratio of total interior angles to total exterior angles of a quadrilateral is
Select one:
a. 3:1
b. 1:2
c. 1:1
d. 2:1
9514 1404 393
Answer:
c. 1 : 1
Step-by-step explanation:
The total of exterior angles of any convex polygon is 360°. The total of interior angles of a quadrilateral is 360°. So, the ratio of interest is ...
interior : exterior = 360° : 360° = 1 : 1
Karen is having a party. She'll have 4 tables for every 12 guests. Complete the table below showing the number of tables and the number of guests.
A car which was advertised for sale for 95000, was ultimately sold for 83600. Find the percent reduction in the price?
Answer: 12%
Step-by-step explanation:
95,000-83,600=11,400
(11,400/95000)(100) = 12%
The percentage reduction in the price of the car is 12%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Original price of car=95000 and Selling price=83600
Thus the reduction in price= 95000-83600
=11400
Thus percentage reduction in the price of the car is
= 11400/95000 × 100
=12%
Hence, The percentage reduction in the price of the car is 12%
Learn more about percentages here:
https://brainly.com/question/29306119
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Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5
Solution :
Here the probability that exactly 28 out of 304 students will not graduate on time. That is
P (x = 28)
By using the normal approximation of binomial probability,
[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]
∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]
[tex]$=P(27.5 \leq x \leq 28.5)$[/tex]
That is the area between 27.5 and 28.5
Therefore, the correct option is (e). Area between 27.5 and 28.5
Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 30% of the passengers are on business while on ordinary jets 25% of the passengers are on business. Of Global's air fleet, 60% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.)
a) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Answer:
a) 0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.
b) 0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
Event A: Jumbo
Event B: Business
60% of its capacity is provided on jumbo jets.
This means that [tex]P(A) = 0.6[/tex]
On jumbo jets, 30% of the passengers are on business
This means that [tex]P(B|A) = 0.3[/tex]
Desired probability:
We want to find [tex]P(A \cap B)[/tex], so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.6*0.3 = 0.18[/tex]
0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.
b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?
Event A: Ordinary
Event B: Non-business
60% of its capacity is provided on jumbo jets.
So 100 - 60 = 40% are ordinary, which means that [tex]P(A) = 0.4[/tex]
On ordinary jets 25% of the passengers are on business.
So 100 - 25 = 75% are non-business, that is [tex]P(B|A) = 0.75[/tex]
Desired probability:
We want to find [tex]P(A \cap B)[/tex], so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A) = 0.75*0.4 = 0.3[/tex]
0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.
3. You buy butter for $3 a pound. One portion of onion compote requires 2 oz of butter. How much does the butter for one portion cost?
Answer:
The butter for one portion cost $ 0.375.
Step-by-step explanation:
Given that you buy butter for $ 3 a pound, and one portion of onion compote requires 2 oz of butter, to determine how much does the butter for one portion cost, the following calculation must be performed:
2 oz = 0.125 lb
1 = 3
0.125 = X
3 x 0.125 = X
0.375 = X
Therefore, the butter for one portion cost $ 0.375.
According to the Federal Election Commission, 53.6% of all registered voters in 2012 voted in the US presidential elections in 2012. A political study conducted in January 2016 surveyed 1,251 eligible voters and found that 86% said they planned to vote in the 2016 presidential election. Based on this information, match each term to its value.
1. 1,251
2. 53.6%
3. 86%
a. statistic
b. sample size
c. parameter
Answer:
SEE BELOW
Step-by-step explanation:
1. sample size - 1,251
2 .statistic - 53.6%
3. parameter - 86%
hope this helps :)
plz help I will give Brianly
A pair of linear equations is shown below: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points) Select one: a. On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. b. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. c. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. d. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
the answer is 89
Step-by-step explanation:
this is a hard one to salve but basically if you know and lern hout to do it it is not that hard
in the box of Stones ,the ratio of red marbles is 2:5. the ratio of green stones to the total stones is 3:10 .if the stones that are neither red nor green are blue ,how many blue are in the box.if there are 40 marbles in the box?.
What is the solution to this system of equations?
a - b + c = -6
b - c = 5
2a - 2c = 4
A) 2
B) -1
C) -3
D) 1
(-1;2;-3)
а, b, c
~~~~~~
How many mL of a 10% magnesium sulfate solution will contain 14 grams of magnesium sulfate?
Answer:
Upto 40 g or 160 mmols
Step-by-step explanation:
Can you plz mark me as brainliest?
Answer:
140 mL
Step-by-step explanation:
10% of 140 is 14
Two six sided dice are rolled. What is the probability of one of those being a 4?
2) Find the missing digit for the following bank identification numbers:
a. 71100139
b. 321000 56
Answer:
i donno
Step-by-step explanation:
i
Please help me to find this answer
Answer:
Look in Step by Step Explanation
Step-by-step explanation:
3)SOHCAHTOA
tan=opposite/adjacent
tan(20)=x/83
83tan(20)=x
x=30.209
2) SOHCAHTOA
Tangent=opposite/adjacent
Tan(62)=x/8
8tan(62)=x
x=15.04
3)SOHCAHTOA
Sin=opposite/hypotonouse
sin(25)=30/x
x=30/sin(25)
x=70.986
Raj wants to get a tropical fish tank. The pet store owner tells him that he needs a tank that has a total volume equal to 80 ounces plus 4 ounces for each fish.
Which model shows two expressions for the total volume of the tank that will hold f fish?
A. 2(2e + 4f + 10g)
B. 80(e + f + g)
C. 2(2e + 2f + 5g)
D. 2(e + 2f + 5g)
Answer:
A. 2(2e + 4f + 10g)
Step-by-step explanation:
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
If a^2+b^2= 4 and ab = 5, what is the value of
(a+b)^2?
A. 10
B. 12
C. 14
D. 16
Answer:
14
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
FOIL
a^2 + ab+ab + b^2
Combine like terms
a^2 +2ab + b^2
Rearranging
a^2+b^2 +2ab
We know a^2+b^2 = 4 and ab= 5
4 + 2(5)
4+10
14
Answer:
C. 14.
Step-by-step explanation:
We use the identity:-
a^2 + b^2 = (a + b)^2 - 2ab
So 4 = (a + b)^2 - 2(5)
(a + b)^2 = 4 + 2(5)
= 14.
Choose the expression that represents “divide 0.04 by n.”
Answer:
.04/n=4/100n or 4÷100n
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
please answer quick i need to go to my friends to get my joy con fixed
The area is just the base times the height. In this case, the base is (x+4) and the height is (x+6), and then you just distribute to get x^2 +4x+6x+24 which is x^2+10x+24.
A distribution of values is normal with a mean of 1986.1 and a standard deviation of 27.2.
Find the probability that a randomly selected value is greater than 1914.8.
P(X> 1914.8) =
Enter your answer as a number accurate to 4 decimal places. *Note: all z-scores must be rounded to
the nearest hundredth.
Answer:
I used the function normCdf(lower bound, upper bound, mean, standard deviation) on the graphing calculator to solve this.
Lower bound = 1914.8Upper bound = 999999Mean = 1986.1Standard deviation = 27.2Input in these values and it will result in:
normCdf(1914.8,9999999,1986.1,27.2) = 0.995621
So the probability that the value is greater than 1914.8 is about 99.5621%
I'm not sure if this is correct 0_o
Help me please and thank you
Step-by-step explanation:
jlejej
are u using chrome os
Hi! I would appreciate if you could solve this for me. The question I need help with is question 41. Thank you. :)
Answer:
Expression: 7+7+9.5+6+9.5
Evaluation: 39 cm
Step-by-step explanation:
Let's write the numerical expression for the figure to the right. The perimeter is the addition of all sides of the figure. Therefore, we write 7+7+9.5+6+9.5 for our expression.
Now, to evaluate the expression, we just add them together. 7+7+9.5+6+9.5=39 cm.
Suppose you are starting your own company selling chocolate covered strawberries. You decide to sell the milk chocolate covered strawberries for a profit of $2.25/box and the white chocolate covered strawberries at $2.50/box. Market tests and available resources, however, have given you the following constraints. The combined production level should not exceed 800 boxes per month. The demand for the white chocolate is no more than half the demand for milk chocolate strawberries. The production level for white chocolate should be less than or equal to 200 boxes.
Using the information in the problem, write the constraints. Let x represent number of milk chocolate boxes produced, and y represent number of white chocolate boxes produced.
Total number of chocolate boxes that can be produced: x+y Answer
≤
Answer
800
Restrictions based on demand of each: y Answer
Answer
200
x
Maximum amount of white chocolate production: y Answer
≤
Answer
200
Minimum amount of milk chocolate production: x Answer
Answer
Minimum amount of white chocolate production: y Answer
Answer
Vertices of the feasible region: (0,0)(400, Answer
)( Answer
, Answer
)( Answer
,0)
Optimization equation: Profit = Answer
x+ Answer
y
Your maximum profit is $ Answer
. You should produce Answer
boxes of milk chocolate and Answer
boxes of white chocolate.
Answer:
Step-by-step explanation:
I answered this question in question #24285520
Answer:
Step-by-step explanation:
Total number of chocolate boxes that can be produced: x+y Answer
≤
Answer
800
Restrictions based on demand of each: y Answer
≤
Answer
1/2
x
Maximum amount of white chocolate production: y Answer
≤
Answer
200
Minimum amount of milk chocolate production: x Answer
≥
Answer
0
Minimum amount of white chocolate production: y Answer
≥
Answer
0
Vertices of the feasible region: (0,0)(400, Answer
200
)( Answer
600
, Answer
200
)( Answer
800
,0)
Optimization equation: Profit = Answer
2.25
x+ Answer
2.5
y
Your maximum profit is $ Answer
1850
. You should produce Answer
600
boxes of milk chocolate and Answer
200
boxes of white chocolate.
Aku has less than 3 times as many mangoes as Alaba and half as many mangoes as Amina if alaba has x mangoes the interns of x then how many mangoes do aku alaba and Amina have in combined
Answer:
I have no clue my bad bro.
Determine what type of transformation is represented.
A. none of these
B. reflection
C. dilation
D. rotation
Answer:
The answer is "Option D"
Step-by-step explanation:
In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.
