Answer:
0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g
Step-by-step explanation:
To solve this question, we use 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 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.
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.
Mean weight of 67g and a sample standard deviation of 1g.
This means that [tex]\mu = 67, \sigma = 1[/tex]
Sample of 4
This means that [tex]n = 4, s = \frac{1}{\sqrt{4}} = 0.5[/tex]
What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?
This is the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 67}{0.5}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g
Answer:
-10
Step-by-step explanation:
Khan
Convert 2.88 x 10-12 into standard notation
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Answer: IF you meant 2.88 x 10^-12 The answer is: 0.00000000000288 OTHERWISE i don't know what you were asking
Explanation:
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:1.6799999999999997 x 10^1
There was 7L punch for the birthday party. How many mL punch was there?
Answer:
7000 milliliters of punch for the birthday party
2.5
pocket money in the ratio 6:5. Calculate Jannie's adjusted monthly pocket money.
Khaya is delivering groceries to his mother who stays 8km from the shop. How long will it take him
to cover this distance if he drives at an average speed of R65km/h? Give your answer rounded to the
nearest minute.
Answer:
pzie6zkezkzorzozirusultaluspuar
what is the square root of 7875
Answer:
7875−−−−√225⋅35−−−−−−√ 225−−−√35−−√ 1535−−√
7875−−−−√=88.74119674649424
hope that helps!
As you know, there are three doors. Behind one door is a fabulous prize.
Behind the other two doors are bogus prizes. When you pick the first door
another door will open and show you a bogus prize, leaving the door you
picked and the third door closed. You once again pick one of the two closed
doors. You will either get the fabulous prize or the bogus prize
Answer:
What do you mean
Step-by-step explanation:
Select the correct answer.
Choose the number sentence that illustrates the distributive property of multiplication over addition.
6 × (5 + 8) = (6 × 5) + 8
6 × (5 + 8) = (6 + 5) × (6 + 8)
6 × (5 + 8) = (6 × 5) + (6 × 8)
Answer:
Probably B.
Step-by-step explanation:
What are the first six multiples of 18
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer.....
The first six multiples of 18 are :-
18, 36, 54, 72, 90, 108Hope it helps!
mark me brainliest plz....
Follow me! :)
Myopia in children. Myopia, also called short-sightedness, is a common visual impairment that is reaching alarming proportions worldwide. The condition typically develops in school-age children and adolescents. It has long been thought that the condition was associated with too much reading, but recent evidence suggests instead that a lack of exposure to natural outdoor light may play a role. To investigate this new theory, researchers compared rates of myopia among randomly selected young children (6 and 7 years old) of Chinese ethnicity living in either Sydney (Australia) or Singapore. The researchers found that 4 of the 124 children in the Australian sample had myopia, compared with 183 among the 628 children from Singapore.
a. Display the findings in a two-way table. What percent of the children in the study had myopia? What is that percent among the children living in Australia and among those living in Singapore?
b. The researchers obtained information for most of the children in the study about their weekly amount of time in hours) spent reading or writing and the weekly amount of time in hours) spent on outdoor activities. Here are the summary statistics:
Time reading/writing Number of children Mean Standard deviation
Australia 109 20.8 13.9
Singapore 611 17.8 8.8
Time outdoors Number of children Mean Standard deviation
Australia 102 13.75 1.02
Singapore 586 3.05 0.12
How do the children from both countries in this study differ in how they spend their time?
c. Does the study suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children? Does it suggest that more time spent outdoors is associated with a greater risk of myopia? Can we draw a conclusion of causality based on this study?
d. The children enrolled in this study were all of Chinese ethnicity. What is the advantage in this study of collecting data from children with the same ethnicity compared with selecting random samples of children from each location regardless of ethnicity?
Answer:
a. A two way table is presented as follows;
[tex]\begin{array}{cccc}&Had \ Myopia&Do \ not \ have \ Myopia& Totals\\Sydney \ (Australia)&4&120&128\\Singapore&183&445&628\end{array}[/tex]
ii) The percentage of students in the study that have myopia are approximately 24.867%
iii) The percentage of children living in Australia with myopia are approximately 3.2258%
The percentage of children living in Singapore with myopia are approximately 29.14%
b. Children in Australia spend more time reading, writing and also outdoors than children in Singapore
c. The study does not suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children
The study does not suggests that more time spent outdoors is associated with a greater risk of myopia
d. The advantage is to reduce associated variables the generate more accurate findings or result
Step-by-step explanation:
a. A two way table is presented as follows;
[tex]\begin{array}{cccc}&Had \ Myopia&Do \ not \ have \ Myopia& Totals\\Sydney \ (Australia)&4&120&128\\Singapore&183&445&628\end{array}[/tex]
ii) The percentage of students in the study that have myopia are;
(4 + 183)/(124 + 628) × 100 ≈ 24.867%
iii) The percentage of children living in Australia with myopia is given as follows;
4/124 × 100 ≈ 3.2258%
The percentage of children living in Singapore with myopia is given as follows;
183/628 × 100 ≈ 29.14%
b. The data for the time spent reading and writing is presented as follows;
Number of children [tex]{}[/tex] Mean Standard deviation
Australia 109 [tex]{}[/tex] 20.8 13.9
Singapore [tex]{}[/tex] 611 17.8 8.8
The data for the time spent outdoors is presented as follows;
Number of children [tex]{}[/tex] Mean Standard deviation
Australia 102 [tex]{}[/tex] 13.75 1.02
Singapore [tex]{}[/tex] 586 3.05 0.12
From the data, more children in Australia spend more time reading and writing and also outdoors than children in Singapore
c. From the data, more children spend their time reading and writing in Australia and are also less likely to develop myopia than children in Singapore
Therefore, the study does not suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children
Similarly, the study does not suggests that more time spent outdoors is associated with a greater risk of myopia
d. The advantage of collecting data from children with the same ethnicity compared with selecting random samples of children from each location regardless of ethnicity is to reduce the variables or influential factors that may alter the impact on the test and the results
I need a answer ASAP
Answer:
8
Step-by-step explanation:
y = (10x^2 + 3x^4)/ 2x^2
where x is not equal to 0
(20x + 12x)/4x
32x / 4x
= 8
Amira wrote the inequality p + 5 = 18. Which situation is best represented by this inequality?
Answer: Amira added 5 candy bars to the p pile of candy bars there were no more than 18 candy bars in the pile.
Step-by-step explanation: hope this helps
1. Select all the equations where x = 5 is a solution.* A. 2x + 4 = 14 B. 5x = 55 C. 6x + 3 = 14 D. 8 + 3x = 23 E. 6x = 30 F. 5x = 1
Answer:
A,D,E. Hope this helps!
Step-by-step explanation:
A. x=5
B. x=11
C. x=11/6
D. x=5
E. x=5
F. x=1/5
can somebody help me solve for x.
Answer:
8/3
Step-by-step explanation:
x : 4 = 4 : 6
x = 16/ 6
x = 8/3
PLEASE HELP!!!!!!!!!!! ASAP!!!!!!!!!!!
A freight train from city A to city B and a passenger train from city B to city A left the cities at the same time, at 10:00 AM, heading towards each other. The distance between the cities is 360 miles. The freight train is traveling at 50 mph, the passenger train is traveling at 70 mph.
At what TIME will the trains pass each other?
Answer:
at 1 pm
Step-by-step explanation:
A line's y-intercept is 4, and its slope is 1/2. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = 1/2x + 4
Step-by-step explanation:
The slope-intercept equation is written out like so:
y = mx + b
M stands for your slope: 1/2
B stands for your y-intercept: 4
So, your equation is y = 1/2x + 4
which expression is a factor of x^2-5x-6
Answer:
(x - 6)(x + 1)Step-by-step explanation:
These are the factors
First, find the factors of 6 6 / / \ \ 1 2 3 61 and 6 make 52 and 3 also make 5But which one makes -5-3+2=-1 -2+3=1So not 2 and 3-1+6=5 -6+1=-51 and -6 worksThis means the factors as (x - 6) and (x + 1).Hope this helps,
Kavitha
P.S - Have an awesome day!!
Please help me. I need help
Answer: (2x+11)(x+1)
Step-by-step explanation: 2x 2 +11x+2x+11 then x(2x+11)+(2x+11) and that should get you to (2x+11)(x+1)
Hope this helped :))
what is the solution to the equation 5x = -4?
Answer:
x = -4/5
Step-by-step explanation:
Divide 5 on both sides to isolate x on one side. You get x = -4/5
Answer:
x=-4/5 hope this helps you out math is always hard
Please help me in ASAP
Step-by-step explanation:
code:257 403 0731
Pass:HELLO
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Helpssbwjmeekndhshhsbdh
The nominal resistance of a wire is 0.15 Ohm. Random testing of the wire stock yields the following resistance data:
0.148 0.147 0.151 0.146 0.151 0.148 0.147 0.152
0.151 0.148 0.149 0.147 0.146 0.149 0.151 0.147
Does the sign test yield the conclusion, at the 5% significance level, that the median resistance is less than 0.15 Ohm?
Answer:
The median resistance of the wire is not small than 0,15 Ω at 0,05 of level of significance
Step-by-step explanation:
From data we get x ( sample mean ) s ( sample standard deviation) and n size of the sample
0.148 0.147 0.151 0.146 0.151 0.148 0.147 0.152
0.151 0.148 0.149 0.147 0.146 0.149 0.151 0.147
n = 16
x ≈ 0,1487
s = 0,00193
Test Hypothesis
1.-Null Hypothesis H₀ x = μ₀ = 0,15
Alternative Hypothesis Hₐ x < 0,15
We assume data follows normal distribution
as n = 16 we should use a t-student table
As the question is : "Is the median resistance less than 0,15 0hm " we must use one-tail-test ( to the left)
Then:
2.-Significance level α = 5 % α = 0,05
degree of freedom n = 16 df = n - 1 df = 15
From t-table we find t(c) = 1,7531 at the left is t(c) = - 1,7531
3.-t(s) = ( x - 0,15 ) / s / √n
t(s) = 0,1487 - 0,15 / 0,00193/√16
t(s) = - 0,0013 * 4 / 0,00193
t(s) = - 2,69
4.- Comparing t(s) and t(c)
|t(s) | > |t(c)| 2,69 > 1,753
Then t(s) is in the rejection region
5.- We reject H₀ . At 95 % of confidence Interval
Find the mean, median, mode, and range of the following data set.
15, 12, 19, 15, 16, 13, 15.
Mean:
Median:
Mode:
Range:
12 13 15 15 15 16 19
mean: 15
median: 15
mode: 15
range: 7
Answer:
12, 13, 15, 15, 15, 16, 19
Step-by-step explanation:
Mean: 15
Median: 15
Mode: 15
Range: 7
1809
×308
_____
______
Answer:
557152
Step-by-step explanation:
You first multiply the 8 in 308 to the 9 in 1809, then the 0, then the 9, then finally the 1 in 1809. For the tens place, don't forget to put a zero under the ones place because that's not where you start. So for 0 everything is 0 so just put a line of 5 zeros in the second row. Lastly, the 3 multiplies to 9, 0, 8, and the 1 in 1809. In the 3rd row, put 2 zeros because you're multiplying to get the hundreds place. Line and add them all up to get 557152. Hope this helps!
Answer:
1809 x 308 eqauls 557,172
if you click the image it will show you how to solve the equation step by step. I hope this helps you.
which expression is equivalent to 3(9p+2r)
Answer:
27p+6r
Step-by-step explanation:
3(9p+2r)
1 Solve the product 3(9p+3 2r)
3⋅9p+3x2r
Multiply 3 times 9
27p+3x2r
Final Answer
27p+6r
(Due in 20 minutes)
The three side lengths of four triangles are given. Which triangle is a right triangle?
Triangle 1: √13, 6, 7
Triangle 2: 7, 8, 13
Triangle 3: 10, 11, 12
Triangle 4: √10, 9, 8
A process manufactures ball bearings with diameters that are normally distributed with mean 25.14 mm and standard deviation 0.08 mm. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on
Answer:
The diameter is in the 77th percentile.
Step-by-step explanation:
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 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.
25.14 mm and standard deviation 0.08 mm.
This means that [tex]\mu = 25.14, \sigma = 0.08[/tex]
A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on?
This is the pvalue of Z when X = 25.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25.2 - 25.14}{0.08}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a pvalue of 0.77.
The diameter is in the 77th percentile.
Help pls
Reasoning Each month, a shopkeeper spends 7x +19 dollars on rent and electricity. If he spends
5x – 2 dollars on rent, how much does he spend on electricity? Use pencil and paper. For which
value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you
found the value(s).
The amount spent on electricity is 2x + 21. And the value(s) of x is the amount the shopkeeper spends on electricity less than $100 is less than 39.5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Reasoning Each month, a shopkeeper spends 7x +19 dollars on rent and electricity. If he spends 5x – 2 dollars on rent.
Then the amount spent on electricity is given as,
⇒ (7x + 19) - (5x - 2)
⇒ 7x + 19 - 5x + 2
⇒ 2x + 21
The value(s) of x is the amount the shopkeeper spends on electricity less than $100 is given as,
2x + 21 < 100
2x < 79
x < 39.5
The amount spent on electricity is 2x + 21. And the value(s) of x is the amount the shopkeeper spends on electricity less than $100 is less than 39.5.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
If -5x-y=1 is a true equation, what would be the value of 5(-5x-y)?
Answer:
-25-5x-5y
Step-by-step explanation:
(60 points)!
What type of angles are ∠4 and∠6?
Question 2 options:
adjacent angles
alternate exterior angles
alternate interior angles
corresponding angles
none of these
When we take two parallel lines they will create 8 angles, such as 1,2,3,4,5,6,7 & 8. In that angle 6 is 65 degrees. Angles 1,2,3 & $ are in one line and remaining four angles on other line. So Angles 4 and 6 are alternate exterior angles.
20% of ___ is 10 pls help me ✌
Answer:
200
Step-by-step explanation:
i hope this is right if not sorry
consider the absolute value functions c and d
which statement correctly describes these functions?
A.The maximum value of d is 5 less than the minimum value of c
B. The maximum value of d is 3 less than the maximum value of c.
C.The minimum value of d is 5 more than the maximum of c
D. The minimum value of d is 3 more than the maximum of value c.