Answer:
The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are 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.
In this problem, we have that:
[tex]\mu = 5.2, \sigma = 0.08, n = 20, s = \frac{0.08}{\sqrt{20}} = 0.0179[/tex]
Find the interval that contains 95.44 percent of the sample means.
0.5 - (0.9544/2) = 0.0228
Pvalue of 0.0228 when Z = -2.
0.5 + (0.9544/2) = 0.9772
Pvalue of 0.9772 when Z = 2.
So the interval is from X when Z = -2 to X when Z = 2
Z = 2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2 = \frac{X - 5.2}{0.0179}[/tex]
[tex]X - 5.2 = 2*0.0179[/tex]
[tex]X = 5.2358[/tex]
Z = -2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 5.2}{0.0179}[/tex]
[tex]X - 5.2 = -2*0.0179[/tex]
[tex]X = 5.1642[/tex]
The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches
The following question has two parts. First, answer part A. Then, answer part B.
Isabella's mother has a garden with a total area of
10/23 square feet. She plans her planting season like this:
1/4 of the garden will be used for planting peas. And,
3/4 of the garden will be used for planting corn.
Find the length of a rectangle with area of 16 sq. cm. and width of 8 cm.
2 cm
8 cm
128 cm
how many solutions 2x+3y=-3 and 3x + 5y = -9
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Four gallons of paint are used to paint 25 chair. If each chair used the same amount of paint how many gallons are used to paint each chair? Between what two whole number does your answer lie
WILL GIVE BRAINLIEST!!!!!!!!!!!!!! Select the points that are solutions to the system of inequalities. Select all that apply
The points that are solutions to the system of inequalities is ( -12,0), (-10,1), the correct option is A and C.
What is System of Inequalities?The system of Inequalities are the set of inequalities that have a common solution.
The solution of the set of Inequalities can be obtained by plotting a graph and finding the common area.
The solution to the system of inequalities is shown in the graph.
The points that are solutions to the system of inequalities is
( -12,0)
(-10,1)
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Two jets leave an airport at the same time, flying in opposite directions. The first jet is traveling at three hundred seventy-seven mph and the other at two hundred seventy-five mph. How long will it take for the jets to be 9128 miles apart?
Cereal is packaged in a box shaped like a rectangular prism with a base 7.5 by 2 inches, and a height of 10 inches. Manufacturing each box requires 10% more cardboard than the box’s surface area. How much cardboard is needed to make each box
In a right triangle a=2b+4 and all side lengths are integers. The possible values for b are 4cm, 5cm, 8cm,10cm,12cm,and 24cm. Determine the values for a,b, and c. For the right triangle, a is ______cm long, b is _________cm long, and c is __________cm long. Create a similar triangle with different side lengths. Draw and label the side lengths.
Please help, math question.
Identify the variable and the categories represented in this problem. Set up and fill in a two-way table to represent the frequencies in this problem.
Explain how you know 21/100 is greater than 1/5
This problem can be solved using equivalent fractions. The first step in resolving this problem is to realize that fractions are best compared when they both have the same denominator. In this case, I will choose to make that common denominator 100. There is no need to rewrite the fraction [tex]\frac{21}{100}[/tex] as the denominator for this fraction is already 100. The fraction [tex]\frac{1}{5} =\frac{20}{100}[/tex] . This is achieved by multiplying both the numerator and denominator by 20. Now that the two fractions have the same denominator, we can easily see that [tex]\frac{21}{100}[/tex] is greater than [tex]\frac{1}{5}[/tex] because it is greater than its equivalent fraction.
A 60 kg dog requires fluids at 50 mL/kg over 24 hours. Using a 10 gtt/mL set how many gtts/min will you set?
To set the infusion rate for a 60 kg dog, calculate the total fluid needed (3000 mL), the total number of drops (30,000 gtts), and then determine the drops per minute (20.83 gtt/min), rounding to approximately 21 drops per minute.
To calculate the infusion rate for a 60 kg dog that needs 50 mL/kg of fluids over 24 hours using a 10 gtt/mL set, follow these steps:
Firstly, calculate the total volume of fluids required by the dog:Therefore, you will set the infusion to approximately 21 drops per minute (rounding to the nearest whole number).
A triangle shaped paper’s height is 18 cm and width is 10 cm. Find the hypotenuse of the paper.
The hypotenuse of the paper is 2√106 cm.
What is Pythagorean theorem ?
Hypotenuse ² = Height ² + Width ²
Know more about Pythagorean theorem,
The Pythagorean Theorem, also known as the Pythagoras Theorem, explains the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. Pythagorean triangles are the name given to the sides of a right triangle. Let's learn about Pythagorean theorem, formula, derivation and examples in detail.
The history of the Pythagorean theorem goes back to the ancient Babylonian and Egyptian era. The Greek mathematician Pythagoras of Samos introduced the Pythagorean theorem. Pythagoras was born in 570 BC. The Greek philosopher studied with other monks and formed a group of people; he finally stated the Pythagorean theorem. Even before Pythagoras, the ratio was shown on a Babylonian tablet 4000 years ago, but the theorem is published under the name of Pythagoras.
Here given, a triangle shaped paper’s height is 18 cm and width is 10 cm.
We want find the hypotenuse of the paper ?
Here, height of the paper = 18 cm and width of the triangle = 10 cm.
[tex] = {18}^{2} + {10}^{2} \\ = 324 + 100 \\ = 424[/tex]
So,
[tex]hypotenuse = \sqrt{424} \\ = \sqrt{2 \times 2 \times 2 \times 53} \\ = 2 \sqrt{2 \times 53} \\ = 2 \sqrt{106} \: cm[/tex]
Therefore,the hypotenuse of the paper is 2√106 cm.
Pythagoras theorem related one more question:
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Leanne can clean a fish tank in 30 minutes. Karl can clean a fish tank in 20 minutes. If they work together, how many minutes does it take them to clean a fish tank? (2 points)
Answer:
12 minutes
Step-by-step explanation:
Just took the test and got it right
Honi is looking at a map with a scale of 1 4 in. = 20 miles. She measured the distance from Niceville to Live Oak as 2.5 in. She found the actual distance between Niceville and Live Oak by following these steps:
Step 1: Set up a proportion 1 4 20 = 2.5 x
Step 2: Cross multiply (20)(2.5) = ( 1 4 )(x)
Step 3: Simplify 50 = 1 4 x
Step 4: Solve for x, x = 250 miles
Which step, if any, contains a mistake?
A) Step 1
B) Step 2
C) Step 3
D) Step 4
The mistake is in Step 4 of Honi's calculation. The correct actual distance between Niceville and Live Oak should be 200 miles instead of the 250 miles that was stated in the original steps.
Explanation:The student's question pertains to setting up and solving a proportion to find the actual distance between two places using a map scale. The map scale given is ¼ in. = 20 miles. Honi measures a distance of 2.5 inches on the map. The steps to find the actual distance, using a proportion, should be evaluated for accuracy.
To set up the proportion correctly, we use the ratio of the map scale and compare it to the ratio of the measured distance to the actual distance (x). The correct proportion should be: (1/4 in.) / 20 miles = 2.5 in. / x miles.
Step 1 is correct, setting up the proportion based on the scale and measured distance. Step 2 involves cross-multiplying to find the relationship between the scale and the actual distance, which should yield (1/4) * x = 2.5 * 20. Step 3 should simplify this equation correctly, which would give us x = 2.5 * 20 * 4 = 200 miles. Therefore, Step 4 has a mistake because the solution provided should be 200 miles, not 250 miles as given.
Can you please help me?
what is the length of AC?
Which of the following graphs represents the equation x >-3y+9
Find the number that is smaller than 5 5/12 by as much as 2 2/13 is smaller than 6 1/6
Answer: the number is x = 1 + 21/52
Step-by-step explanation:
we have
(5 + 5/12) - x = (6 + 1/6) - (2 + 2/13)
this means that x is smaller than 5 + 5/12 by the same amount as (2 + 2/13) is smaller than (6 + 1/6)
We can solve it directly, first solve the parentheses, put the whole numbers at one side and the fractions in the other side:
5 - 6 + 2 - x = -5/12 + 1/6 - 2/13
1 - x = -5/12 + 2/12 - 2/13
1 - x = -3/12 - 2/13 = -1/4 - 2/13 = -13/(4*13) - (2*4)/(4*13) = -21/52
x = 1 + 21/52
Answer:
73/52
Step-by-step explanation:
If carleys mows the lawn for 2 weeks Ina row and does her chores 7 weeks straight how many more weeks will she need
Help please help I need help please like pretty please btw this is on mobile
Which of these examples is an error of addition by one?
A. 46,371 + 32,618 = 78,989
B. 38,273 + 51,425 = 89,798
C. 13,246 + 84,631 = 97,877
D. 52,634 + 25,145 = 77,779
Answer: B. 38,273 + 51,425 = 89,798
Step-by-step explanation:
Let's check all the sum by adding their corresponding places.
A. [tex]46,371 + 32,618 = 78,989[/tex]
Its correct.
B. [tex]38,273 + 51,425 =89698\neq 89,798[/tex]
Here when we add the digits on the hundredth place we get 6 not 7.
Hence, it is the example of an error of addition by one.
Its correct.
C. [tex]13,246 + 84,631 = 97,877[/tex]
Its correct.
D. [tex]52,634 + 25,145 = 77,779[/tex]
Its correct.
which values are solutions to the inequality below? check all that apply
a step on a stairway is at least 8 inches high. Write and solve an inequality to represent the minimum number of steps between floors that are 10 feet apart
Answer:
If a step is "at least" 8 inches high, the minimum number of steps is theoretically 1, because that 1 step could be a 10-foot high step.
Step-by-step explanation:
In which graph does y vary directly as x? It’s not C, I got it wrong.
If we consider the toss of four coins as an experiment, how many equally likely outcomes does the sample space have?
The no. of equally likely event is 10.
What is probability ?Probability is chance of occurrence of a certain event out of all the possible events that can occur in a given situation.
According to the given question Tossing of four coins simultaneously as an experiment let us find he sample space and assuming that all these 4 coins are unbiased.
S = { HHHH, HHHT, HHTT, HTTT, TTTT, TTTH, TTHH, THHH, HTTH, THHT }.
∴ N(s) = 10.
As these 4 coins are unbiased there for all the events in the sample space are equally likely to happen.
So, The no. of equally likely outcome is 10.
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find the 8th term of the expansion of (1/2x-y)^10
a 5x^3y^7
b 70x5y5
c -14x3y7
d -15x3y7
Answer:
d. [tex]-15x^3y^7[/tex]
Step-by-step explanation:
By the binomial theorem,
[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r} q^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Thus,
[tex](\frac{1}{2}x-y)^{10}=(\frac{x}{2}+(-y))^{10})=\sum_{r=0}^{n} ^10C_r (\frac{x}{2})^{10-r} (-y)^{r}[/tex]
For the 8th term, r = 7,
Thus, the 8th term would be,
[tex]^{10}C_7 (\frac{x}{2})^{10-7} (-y)^{7}[/tex]
[tex]=\frac{10!}{7!(10-7)!} (\frac{x}{2})^3 (-y)^7[/tex]
[tex]=-\frac{10\times 9\times 8}{3\times 2\times 1}\times \frac{x^3}{8}\times y^7[/tex]
[tex]=-\frac{720x^3y^7}{48}[/tex]
[tex]=-15x^3y^7[/tex]
Hence, option 'D' is correct.
please helppp its too hard!!!
A farmer raises chickens and cows. There are 34 animals in all. The farmer counts 110 legs on these animals. How many of each animal does the farmer have?
The angle of inclination of a ramp is 6° and the ramp is 14 feet long. Approximately how high off the ground is the end of the ramp? 0.8 ft 1 ft 1.5 ft 1.8 ft
Answer:
1.463 ft.
Step-by-step explanation:
As you can see in the image, we can use the sin(6) to calculate the high.
sin(6°) = x/14
x = sin(6°)*14
x = 1.463 ft.