Answer:
0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.
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.
Mean 790 and standard deviation 92.
This means that [tex]\mu = 790, \sigma = 92[/tex]
Samples of 98
This means that [tex]n = 98, s = \frac{92}{\sqrt{98}}[/tex]
What is the probability that the mean number of eggs laid would differ from 790 by less than 30?
This is the pvalue of Z when X = 790 + 30 = 820 subtracted by the pvalue of Z when X = 790 - 30 = 760. So
X = 820
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{820 - 790}{\frac{92}{\sqrt{98}}}[/tex]
[tex]Z = 3.23[/tex]
[tex]Z = 3.23[/tex] has a pvalue of 0.9994
X = 760
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{760 - 790}{\frac{92}{\sqrt{98}}}[/tex]
[tex]Z = -3.23[/tex]
[tex]Z = -3.23[/tex] has a pvalue of 0.0006
0.9994 - 0.0006 = 0.9988
0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.
Find the common ratio of the geometric sequence 6 , 24 , 96 , . . .
Answer:
4
Step-by-step explanation:
6 * 4 = 24
24 * 4 = 96
The original price of a book is $25. The book is on sale for 30% off.
What percent of the price are we paying? What is the price you will pay
for the book?
Answer:
You will pay 70% of the original price. You will pay $17.50
Step-by-step explanation:
100% is full price because 100%=1 (one whole).
100% - 30% = 70%
70% = 0.7
0.7 multiplied by $25 is $17.50
Sum the following numbers then divide by 5
( 3 + 5 + 6 + 2 + 4 ) /5 } = ? What is your answer ?
Answer:
4
Step-by-step explanation:
(3+5+6+2+4) / 5 = ?
(20) / 5 = 4
Points R, S, T, and U lie on circle O.
R
S
o
U
© 2016 StrongMind Created using GeoGebra.
In circle 0. ZROSTOU, RS = 12x + 4 and TU=112 + 15.
What is the length of TU?
Answer:
136
Step-by-step explanation:
12x + 4 = 11x + 15 {Subtract 11x from both sides.}
(12x - 11x) + 4 = 15
x + 4 = 15 {Subtract 4 from both sides.}
x = 15 - 4
x = 11
Now, SUBSTITUTE 11 for x in 11x + 15.
11(11) + 15
121 + 15
136 units
The length of line TU is 136 units.
A circular grade has a circumference of 38 yards .Lars is digging a straight line along the diameter of the garden at a rate of 3 yards.How many hours will it take to dig acceso the garden?
Answer:
It will take 4 hours to dig access to the garden.
Step-by-step explanation:
Given that a circular grade has a circumference of 38 yards, and Lars is digging a straight line along the diameter of the garden at a rate of 3 yards, to determine how many hours it will take to dig access to the garden, the following calculation, knowing that the diameter of a circle is equal to the circumference divided by π:
38 / π = X
38 / 3.14 = X
12.09 = X
12.09 / 3 = 4.03
Therefore, it will take 4 hours to dig access to the garden.
Find X and Y, THIS IS DUE VERY SOON, PLEASE HELP!
Answer:
X is equal to 8, and Y is equal to 35
Step-by-step explanation:
You'll use the Pytagoras theorem to find the values of X and Y.
write the sum 3+3+3+3+3+3 using sigma notation
Answer:
18
Step-by-step explanation:
The sum 3+3+3+3+3+3 can be write using sigma notation [tex]\sum_{i=1}^{6}3[/tex] .
What is sigma notation?A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum.
According to the question
The sum 3+3+3+3+3+3
Represent the sum as sigma notation
[tex]\sum_{i=1}^{6}3[/tex] start at 1 and goes up to 6
= 3+3+3+3+3+3
Hence, the sum 3+3+3+3+3+3 can be write using sigma notation [tex]\sum_{i=1}^{6}3[/tex] .
To know more about sigma notation here:
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Here are some points. What is 2/5 out of twenty?
Answer:
8
Step-by-step explanation:
You just need to multiply 20 by 2/5
Or, multiply 20 by 2, then divide by 5.
20 x 2/5
40/5
8
2/5 of 20 = 40/5 or simply, 8.
Have a great day!
Ryan needs 20 feet of cable. The longest piece on her truck is 18 3/8 feet. How many feet too short is the cable on the truck? *
Answer:
1 5/8 too short
Step-by-step explanation:
The cable on the truck is 18 and 3/8 ... to complete the fraction into a whole number we would need 5 more parts in order to complete the entire 8 parts of the fraction. This would make the cable a whole 19 feet. Since Ryan needs 20 ft, this would leave us needing 1 more foot. Therefore, the cable in the truck is
1 5/8 too short
Giving brainliest!!!!!!
Answer:
Answer should be 6, I think
Kate asked her friend what her favorite class at school is  how could she changed her questioning so that she can collect statistical data
Answer:
If Kate is trying to ask multiple people, Making a bar graph would be smart in order to know how much people liked what.
Step-by-step explanation:
Kate could ask all of the sixth grade students what their favorite class is.
What is a Statistical Data?Statistical data is defined as the data which are collected and interpreted in statistics.
These data are the information about something.
Given that,
Kate asked her friend what her favorite class at school is.
In order for her to collect statistical data, there must be more data related to the same question.
Then she can interpret the data with a conclusion.
So, she has to ask more people the same question that she asked with her friend.
So she could ask all of the sixth grade students what their favorite class is.
Hence the question can be changed as Kate could ask all of the sixth grade students what their favorite class is.
Learn more about Statistical Data here :
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50 POINTS PLEASE HELP!!! Use the formula Circumference = 2nr, where r is the radius and a is 3. 14, to answer the question.
3.0 cm
What is the approximate circumference of the circle?
A 6.00 cm
B. 9.42 cm
C 18.84 cm
D 37.68 cm
Answer:
This one is easy I did this one before its A
Answer:
the answer is c
you times the radius with the 2 and the pi
Write impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0,close to 0, 1/2, close to 1, or 1 Picking a red marble from 4 white marbles and 7 green marbles
Answer:
Step-by-step explanation:
What is the value of (5)3?
Answer:
15
Step-by-step explanation:
This is simply just 5 x 3 = 15
32 1/2 meters to feet
Answer:
106.6273
Step-by-step explanation:
Answer:
106.6273 ft
Step-by-step explanation:
I really want to know what 2+2 is.
Answer:
Step-by-step explanation:
4
Answer:
It's 4 for you and 5 points for me
Step-by-step explanation:
A muralist is painting the side wall of a building. The wall is shaped like a rectangle that is 60
feet long and has a diagonal length of 68 feet. If a gallon of paint can cover 800 square feet,
how many gallons will the muralist use?
Answer:
2.4 gallons
Step-by-step explanation:
to answer this question :
we have to determine the width of the rectangle.
determine the area
determine the gallons needed
Pythagoras theorem would be used to determine the width of the wall
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
60² + b² = 68²
3600 + b² = 4624
b = ²4624 - 3600 = 1024
√b = 32
Area of a rectangle = length x width
32 x 60 = 1920
Gallons needed = 1920 / 800 = 2.4 gallons
What is the volume, in cubic meters, of a rectangular prism with a height of 14 meters, a width of 17 meters, and a length of 13 meters?
Answer: 3084
Step-by-step explanation: 14•17=238 238•13=3084
Answer:
3094
Step-by-step explanation:
l=13 w=17 h=14
v = L W H
V= ( 13 ) ( 17 ) ( 14 )
V= 3094 meters 3
Your Solution:
V= 3094
Solve the equation. 2cos2(x+30°)=1 for 0°≤x≤360°
2*[tex]cos(x+30)^{2}[/tex]=1
x = 15
Then Find The Value Of X
Answer:
15
Step-by-step explanation:
The given is a right triangle divided into two parts by a sector
so 3x + 45 = 90 subtract 45 from both sides
3x = 45 divide both sides by 3
x = 15
This recipe makes 6 portions of fajitas.
Carly has 900 g of chicken, 1200 g of peppers, 150 g of onion, 60 g of spice mix and 30 tortillas.
How much more of each ingredient will she need to make 18 portions by following this recipe?
Recipe: Serves 6
500 g chicken
600 g peppers
90 g onion
25 g spice mix
12 tortillas
Answer:
She needs:
600 g chicken
600 g peppers
120 g onion
15 g spice mix
6 tortillas
Step-by-step explanation:
hope this helps and is right. p.s. i really need brainliest :)
What is (8x + 4) added to (15x – 12)?
Answer:
23x-8
Step-by-step explanation:
8x + 15x = 23x
4 + (-12) = -8
Answer:
[tex] \boxed{23x \: – \: 8} [/tex]
Step-by-step explanation:
(8x + 4) added to (15x – 12) =
(8x + 4) + (15x – 12) =
[Group like terms]
(8x + 15x) + (4 – 12) =
[Simplify]
23x – 8
. To test H0: m = 105 versus H1: m ≠ 105, a simple random sample of size n = 35 is obtained. (a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? Why? (b) If x = 101.9 and s = 5.9, compute the test statistic. (c) Draw a t-distribution with the area that represents the P-value shaded. (d) Approximate and interpret the P-value. (e) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, will the researcher reject the null hypothesis? Why?
Answer:
A.) No
B.) test statistic = - 3.108
Check explanation
Step-by-step explanation:
H0: m = 105 versus H1: m ≠ 105
Sample size, n = 35, since we have a large sample size, greater than 30.
B.)
xbar = 101.9 ; s = 5.9
Test statistic :
T = (xbar - μ) ÷ (s/√n)
T = (101.9 - 105) / (5.9/√35)
T = - 3.1 / 0.9972820
Test statistic = - 3.11
Pvalue from Tstatistic, df = 34
Pvalue = 0.003772( Pvalue calculator)
Pvalue is the probability of obtaining a value more extreme or exactly that of the test statistic.
At α = 0.01
Pvalue < α ; We fail to reject the Null
A kangaroo hops 2 kilometers in 3 minutes. At this rate, the kangaroo will travel kilometers in 15 minutes.
Answer:
the kangaroo will travel 10 kilometers
Step-by-step explanation:
15/3=5
5×2=10
Answer:
10
Step-by-step explanation:
We can use the ratio:
3:2
15:?
15/3 is 5
2*5 is 10.
Which of the following tables shows that y is a function of x?
Answer:
Table B
Step-by-step explanation:
Recall: a table of values can only represent a function if and only if every x-value has exactly only one y-value.
The only table that satisfies this condition is the table in option B.
In table B, every x-value is related to only exactly one y-value.
Laurie is working on a carpentry project. She has n feet of wood. While working, she realized that she needs 1/4
more wood than she currently has. Which expressions represent the total amount of wood she needs for her project? Select all that apply.)
A.n+1/4
B.5/4n
C.1/4n
D.5/4+n
E.n+1/4n
Answer:
E because if she needs 1/4 more than what she already has then you have to multiply 1/4 of the wood she already has and add the wood that she already has
Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee at local fast food restaurants. Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg. If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result
Answer:
We would have to take a sample of 62 to achieve this result.
Step-by-step explanation:
Confidence level of 95%.
We have that 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 Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue 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.
Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.
This means that [tex]\sigma = 2[/tex]
If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?
We would need a sample of n.
n is found when [tex]M = 0.5[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = 1.96\frac{2}{\sqrt{n}}[/tex]
[tex]0.5\sqrt{n} = 2*1.96[/tex]
Dividing both sides by 0.5
[tex]\sqrt{n} = 4*1.96[/tex]
[tex](\sqrt{n})^2 = (4*1.96)^2[/tex]
[tex]n = 61.5[/tex]
Rounding up
We would have to take a sample of 62 to achieve this result.
After multiplying both the numerators and the denominators, it's time to simplify or
reduce your product.
Example: 2/5x3/4 = 6/20.
The greatest common factor of 6 and 20 is 2. We divide the top and bottom by 2, which
simplifies to 3/10.
What is the reduced product of 2/3 x 5/8?
A
10/24
B
5/12
С
1/2
D
10/12
Answer: The answer is B, 5/12.
hope this helped :)
Answer:
B. 5/12
Step-by-step explanation:
2/3 x 5/8 = 10/24
The greatest common factor of 10 and 24 is 2.
Since the GCF is 2,
We divide the numerator and denominator by 2 and get 5/12.
Therefore, the simplified fraction of 10/24 is 5/12.
find the value of x please help I give brainly
20 points
Answer:
x=148
Step-by-step explanation:
First, find the missing angle by subtracting 100+48 from 180 (all of the angles in a triangle add up to 180). Then, subtract that from 180 (the angles are a linear pair, so they are supplementry, so they add up to 180) x+32=180.
x=148.
(お役に立てれば！)
The perimeter of a rectangle measures 26 in. Find the other
side length, if one side measures 4 in.