Answer:
the probability that 7 out 10 Internet users will order something online is 0.78 or 78%
Step-by-step explanation:
Given that:
Internet users who order something online = 85%
To find:
Probability that 7 out of 10 Internet users will order something online ?
Solution:
This problem is of binomial distribution of probability.
where, p = 0.85
q = 1-p = 0.15
r = 7 and
n = 10
Formula is given as:
[tex]P(x = r) = _nC_r q^{n-r}p^r[/tex]
Putting all the values:
[tex]P(x = 7) = _{10}C_7 0.15^{10-7}\times 0.85^7\\P(x = 7) = _{10}C_3 0.15^{3}\times 0.85^7\\P(x = 7) = 10\times 9 \times 8 \times 0.15^{3}\times0.85^7\\P(x = 7) = 720 \times .0034 \times0.32\\P(x = 7) = 0.78[/tex]
So, the probability that 7 out 10 Internet users will order something online is 0.78 or 78%.
can someone help me plzz!
Answer:
126.6Option A is the right option.
Step-by-step explanation:
Sum of angles in triangle= 180°
[tex]85 + 53 + m < a = 180 \\ or \: 138 + m < a = 180 \\ or \:m < a = 180 - 138 \\ m < a = 42[/tex]
Applying sine rule:
[tex] \frac{sin \: a \: }{a} = \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: (85)}{b} = \frac{sin(42)}{85} \\ 85 \: sin \: (85) = \: b \: sin \: (42) \\ b = \frac{85 \: sin \: (85)}{sin \: 42} \\ ac = 126.6[/tex]
Hope this helps....
Good luck on your assignment...
An article gave the accompanying data on ultimate load (kN) for two different types of beams. Assuming the underlying distributions are Normal, calculate and interpret a 99% Cl for the difference between the true average load for the fiberglass beams and that for the carbon beams.
Type Sample size Sample Mean Sample SD
Fiberglass grid 26 33.4 2.2
Commercial carbon 26 42.8 4.3
grid
1. Calculate and interpret a 99% Cl for true average stance duration among elderly individuals.
2. Carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than younger individuals.
Answer:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.
The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.
The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.
The difference between sample means is Md=-9.4.
[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]
The critical t-value for a 99% confidence interval is t=2.678.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.
[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]
The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:
[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
See more about statistics at brainly.com/question/2289255
Solve this correctly for brainliest !!!!!! 3(7) + 2 • |7 - 8| - 12
Answer:
3(7) + 2* |7 - 8| - 12 = 11
Step-by-step explanation:
3(7) + 2* |7 - 8| - 12
21 + 2* |-1| - 12
21 + 2* 1 - 12
21 + 2 - 12
23 - 12 = 11
Hope this helps! :)
Simply the expression 3.4-1/2(0.75)
Answer:
3.025
Step-by-step explanation:
3.4-1/2(0.75)
3.4-0.375
3.025
Factor completely 5x(x + 3) + 6(x + 3). (1 point)
Answer:
The answer is ( 5x + 6 ) ( x + 3 )Step-by-step explanation:
5x(x + 3) + 6(x + 3)
The final answer is
( 5x + 6 ) ( x + 3 )
Hope this helps you
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis.
There food preferences among vole species are independent of one another. _____
There is a relationship between voles and food preference. ______
To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected:
meadow voles common voles
apple slices 26 32
peanut butter-oatmeal 35 25
When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated.
_____= expected meadow vole/apple slices
_____= expected common vole/apple slices
_____= expected meadow vole/peanut butter-oatmeal
_____= expected common vole/peanut butter-oatmeal
_____= chi-square value
_____= degrees of freedom (whole number only)
_____= using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of alpha=0.05?
_____= will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)
Answer:
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 28.983051
Chi-square value = χ² = 2.154239
Degree of freedom = 1
Critical value = 3.841
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Step-by-step explanation:
He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.
So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Data collected by Dr. Pagels:
meadow voles common voles Row Total
apple slices 26 32 58
peanut butter-oatmeal 35 25 60
Column Total 61 57 118
Where 118 is the grand total.
The expected number is given by
Expected = (row total)×(column total)/grand total
Expected meadow vole/apple slices = 58×61/118
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 58×57/118
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 60×61/118
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 60×57/118
Expected common vole/peanut butter-oatmeal = 28.983051
The chi-square statistic value is given by
χ² = Σ(Observed - Expected)²/Expected
χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051
χ² = 2.154239
The degrees of freedom is given by
DoF = (row - 1)×(col - 1)
For the given case, we have 2 rows and 2 columns
DoF = (2 - 1)×(2 - 1)
DoF = 1
The given level of significance = 0.05
The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be
Critical value = 3.841
Conclusion:
Reject H₀ If χ² > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
For the given case,
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to 6 decimal places as needed
1 meter ≈ 3.28 feet
1 Liter ≈ 0.26 gallons
1 kilogram ≈ 2.20 pounds
33.777 yd ≈ __________ km
Answer:
33.777 yd = 0.030886 km
Step-by-step explanation:
==>Given:
33.777 yd
==>Required:
Convert 33.777 yd to km to 6 decimal places, using the metric and U.S systems.
==>Solution:
To convert, note that 1 km = 1093.6133 yd.
Thus,
1 km = 1093.6133 yd
x km = 33.777 yd
Cross multiply
1 × 33.777 = 1093.6133 × x
33.777 = 1093.6133x
Divide both sides by 1093.6133, to solve for x
33.777/1093.6133 = x
0.03088569 = x
x ≈ 0.030886 (to 6 decimal places)
Therefore, 33.777 yd = 0.030886 km
3a. Write an equation in slope-intercept form of a
line that passes through (2,1) and (6,-5).
Answer:
[tex]y = -3/2x + 4[/tex]
Step-by-step explanation:
[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]
find the value of x that makes abcd a parallelogram
The 4 angles need to add to 360.
2 of them are 70
The other two need to equal 360-140 = 220
They are both the same so one angle needs to equal 220/2 = 110
Now find x:
X + 60 = 110
Subtract 60 from both sides:
X = 50. The answer is D
There are 60 people at the subway station 12 of them jumped the
turnstile. What percentage of people jumped the turnstile? What
percentage of people paid?
Answer:
20% jumped the turnstile
80% paid
Step-by-step explanation:
We can calculate the percent of people that jumped it by dividing the number that did by the total:
12/60 = 0.2, which is 20%
If 20% jumped it, then this means 80% paid.
Answer:
jumped= 20%
paid= 80%
Step-by-step explanation:
[tex]\frac{12}{60}[/tex]×100 = 20%
[tex]\frac{48}{60}[/tex]×100 = 80%
Lisa drew three circles to form a figure. The areas of the circles were in the
ratio 1:4:16. She then shaded some parts of the figure as shown.
What fraction of the figure was shaded?
Answer:
Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]
Step-by-step explanation:
Ratio of the areas of the given circles are 1 : 4 : 16
Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]
= 1 : 2 : 4
If the radius of the smallest circle = x units
Then the radius of the middle circle = 2x units
and the radius of the largest circle = 4x units
Area of the smallest circle = πx²
Area of the middle circle = π(2x)² = 4πx²
Area of the largest circle = π(4x)²= 16πx²
Area of the region which is not shaded in the middle circle = πx²(4 - 1)
= 3πx²
Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded
= 16πx² - 3πx²
= 13πx²
Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]
= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]
= [tex]\frac{13}{16}[/tex]
evaluate 25.1 * 2.51 in two decimal places
Answer:
63.00
Step-by-step explanation:
25.1 × 2.51
Multiply.
= 63.001
Round to two decimal places.
63.00
Answer:
63.00
Step-by-step explanation:
when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00
factorise 12x² + x - 20
━━━━━━━☆☆━━━━━━━
▹ Answer
(3x + 4) * (4x - 5)
▹ Step-by-Step Explanation
12x² + x - 20
Rewrite
12x² + 16x - 15x - 20
Factor out
4x(3x + 4) - 15x - 20
4x(3x + 4) - 5(3x + 4)
Factor
(3x + 4) * (4x - 5)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Which number is greatest? 6.23 times 10 Superscript 12 6.23 times 10 Superscript 8 6.23 times 10 Superscript negative 6 6.23 times 10 Superscript 3
The greatest number is 6.23 times 10 superscript 12.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that the number so;
A.6.23 x 10^12 is equivalent to rolling the decimal 12 times to the right.
B.6.23 x 10^8 is equivalent to rolling the decimal 8 times to the right.
C.6.23 x 10^-6 is equivalent to rolling the decimal 6 times to the left.
D.6.23 x 10^3 is equivalent to rolling the decimal 3 times to the right.
This shows the 10 has been multiplied by itself thrice.
Learn more about scientific notation here:
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Find the area of the yellow region.
Round to the nearest tenth.
15 cm
15 cm
Area = [ ? ] cm2
Answer:
48.3 cm²
Step-by-step explanation:
Let A be the area of the yellow region
A= the area of the square - the area of the quarter square
A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²
0.3y+ z y 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
Answer:
5
Step-by-step explanation:
Substitute the given values and do the arithmetic.
[tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective components is at most .10. The distributor decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2. Let X denote the number of defective components in the sample. What is the distribution of X? Justify your answer.
Required:
What is the probability that the batch will be accepted when the actual proportion of defectives (p) is:_______
a, 0.01
b. 0.05
c. 0.10
d. 0.20
e. 0.25
Answer:
c. 0.10
Step-by-step explanation:
Hello!
To accept a batch of components, the proportion of defective components is at most 0.10.
X: Number of defective components in a sample of 10.
This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)
The distributor will accept the batch if at most two components are defective, symbolically:
P(X≤2)
Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2
P(X≤2)= 0.9298
I hope this helps!
Given X= 5+ V16 select the value(s) of x. Check
all of the boxes that apply.
-11
1
9
21
Answer:
[tex]x = 9\ or\ x = 1[/tex]
Step-by-step explanation:
Given
[tex]x = 5 + \sqrt{16}[/tex]
Required
Find the value of x
[tex]x = 5 + \sqrt{16}[/tex]
We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-
[tex]x = 5 \±4[/tex]
The expression above can be split into two; This is as follows
[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]
[tex]x = 9\ or\ x = 1[/tex]
Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9
Answer:
its b and c
Step-by-step explanation:
the guy who answered first said so
also i just did it
What is the justification for step 2 in the solution process?
Answer:
Answer C
Step-by-step explanation:
You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.
4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these
Answer:
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
Step-by-step explanation:
13 − 01 + 1 = 13
34 − 14 + 1 = 21
56 − 35 + 1 = 22
99 − 57 + 1 + 1 = 44
what is u over 4-4= -20
u/4 - 4 = -20
Add 4 to both sides:
u/4 = -16
Multiply both sides by 4:
u = -64
Answer:
u=-64
Step-by-step explanation:
u/4 -4 = -20
First add 4 to both sides.
u/4=-16
Now multiply both sides by 4
u=-64
what is 3 + 3 × 3 + 3 =
Answer:
15
Step-by-step explanation:
PEMDAS
3x3 = 9
3+3 = 6
9+6 = 15
By the BODMAS rule we get, 3 + 3 × 3 + 3 = 15
The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).
3 + 3 × 3 + 3 =
3 × 3 = 9
3 + 9 + 3 = 15.
Therefore, the correct answer is 15.
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Help please! Simplify 7/ √x
Answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Step-by-step explanation:
To simplify 7/√x, we need to rationalize:
[tex]\frac{7}{\sqrt{x} } (\frac{\sqrt{x} }{\sqrt{x} } )[/tex]
When we multiply the 2, we should get our answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Step-by-step explanation:
[tex]\frac{7}{\sqrt{x} } \\\\\frac{7}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } \\\\\frac{7\sqrt{x} }{\sqrt{x\sqrt{x} } } \\[/tex]
[tex]\frac{7\sqrt{x} }{x}[/tex]
Hope this helps! :)
Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of $176.47 on groceries, $78.66 for phone, and $62.37 on gas. Estimate his monthly total for groceries, phone, and gas by first rounding to the nearest $10.
Answer:
Yearly budget= $3840
Monthly budget= $320
Step-by-step explanation:
His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.
For groceries= $176.47
Round off=$ 180.00
For phone =$ 78.66
Round off = $80.00
For gas = $62.37
Round off= $60.00
His total round off = $180+$80+$60
His total round off = $320
Before the round off, his total spending was $176.47+$78.66+$62.37
= $317.5
So his monthly budget should be $320
And yearly budget =$ 320*12
Yearly budget= $3840
No clue how to graph this any help would be greatly appreciated
Answer:
First, you can graph the y-intercept. The y-intercept would be (0,3) or in your equation, the number 3. Next, you could create a table by substituting values for x such as 1, 2, 3, or 4. This will give you easy numbers to graph. Instead of creating a table, perhaps you want to graph this by plotting the slope. Since the slope is 3/2, is means that it is going up, because the number is positive. An easy way to start would be starting at your y-intercept, (0,3), you could go two to the right and three up. That is a point. Then you could go the way down; two to the left and three down. Finally, you can draw a line connecting the points together.
I hope this helped you! Have a great rest of your day!
Write a pair of integers whose sum is- -8
Answer:
-3+(-5)
Checking our answer:
Adding this does indeed give -8
In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies.
Answer:
A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
Step-by-step explanation:
We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.
Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 94.3
n = sample of car drivers = 16
[tex]\mu[/tex] = population mean number of chips in a bag
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95 {As the critical value of t at 15 degrees of
freedom are -2.131 & 2.131 with P = 2.5%}
P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95
P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]
= [1187.96, 1288.44]
Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
2) Find the diameter.
4) If the diameter is equal to 3 inches ,d=
Answer:
d = 3 in
Step-by-step explanation:
Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.
What is the value of X in equation? 1/3 X - 2/3 = - 18
Answer:
x=-52
Step-by-step explanation:
1/3x=-17 1/3
x=-52
Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d.
Requried:
a. Find a 99% confidence interval for the true mean milk production.
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
Answer:
a) 26.33 kg/d and 29.67 kg/d
b) 94.5%
Step-by-step explanation:
a. Find a 99% confidence interval for the true mean milk production.
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{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
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 = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d
The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d
The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
We need to find z initially, when M = 1.25.
[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]2.25z = 1.25\sqrt{12}[/tex]
[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]
[tex]z = 1.92[/tex]
When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.
1 - 2*(1 - 0.9725) = 0.945
So we should use a confidence level of 94.5%.