Answer:
a) 0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms
b) 0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.
c) 46.24 kilograms
d) The standard deviation would have to be of 3.41 kilograms.
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 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.
Mean of 45 kilograms and a standard deviation of 1.2 kilograms.
This means that [tex]\mu = 45, \sigma = 1.2[/tex]
a. What is the probability that a filled bag will weigh less than 49.5 kilograms?
This is the pvalue of Z when X = 49.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49.5 - 45}{1.2}[/tex]
[tex]Z = 3.75[/tex]
[tex]Z = 3.75[/tex] has a pvalue of 0.9999
0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms
b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?
This is the pvalue of Z when X = 51 subtracted by the pvalue of Z when X = 48.5.
X = 51
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51 - 45}{1.2}[/tex]
[tex]Z = 5[/tex]
[tex]Z = 5[/tex] has a pvalue of 1
X = 48.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48.5 - 45}{1.2}[/tex]
[tex]Z = 2.92[/tex]
[tex]Z = 2.92[/tex] has a pvalue of 0.9982
1 - 0.9982 = 0.0018
0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.
c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
This is the 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 45}{1.2}[/tex]
[tex]X - 45 = 1.037*1.2[/tex]
[tex]X = 46.24[/tex]
46.24 kilograms.
d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?
X = 52 would have to be the 100 - 2 = 98th percentile, which is X when Z has a pvalue of 0.98, so X when Z = 2.054. We would need to find the value of [tex]\sigma[/tex] for this.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{52 - 45}{\sigma}[/tex]
[tex]2.054\sigma = 7[/tex]
[tex]\sigma = \frac{7}{2.054}[/tex]
[tex]\sigma = 3.41[/tex]
The standard deviation would have to be of 3.41 kilograms.
You took out a loan for $15,000 for 3 years with an interest rate of 3.5%. Including interest, how much will you pay total?
Answer:
39%
Step-by-step explanation:
Pls help I'm sleep deprived rn and am almost done with this
Answer:
6π units
Step-by-step explanation:
Given::
Radius = 4
Angle measure of partial circle (θ) = 360° - right angle = 360° - 90° = 270°
Arc length = θ/360 × 2πr
Plug in the values
= 270/360 × 2 × π × 4
= 0.75 × 8 × π
= 6π units
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
jkh and ihk
Step-by-step explanation:
Answer:
<JHK and IHK
Step-by-step explanation:
please help me im stuck on this question
Answer:
78.0 kilo
Step-by-step explanation:
85.8- 93.6= 7.8
101.4-93.6= 7.8
85.8-7.8 = 78.0 kilo
Lincoln Middle School is painting a circle on their playground with a radius of 18 feet. What will be the total area of the circle, in square feet?
Use π = 3.14, and round your answer to the nearest hundredth.
Answer:
1017.36
Step-by-step explanation:
area = 3.14 (18)square
3.14 (324)
1017.36
Question 5: 10 pts
There are 40 pieces of building blocks in a bag. 10 each of blue, green, red, and yellow. Two pieces are chosen
at random. Identify the probability that both of the pieces chosen are green
Answer:
The answer is 3/52
Step-by-step explanation:
These three side lengths make a triangle.
3 cm, 5 cm, 9 cm
A. True
B. False
Answer:
aa
Step-by-step explanation:
aaaaaaaaa i need points sorry
Classify the angle pair using all names that apply
Answer:
Adjacent
Step-by-step explanation:
∠3 and ∠4 share a common vertex & arm
Who can figure out the answer (3 x 1) +(6x 100)=X
Answer:
26
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer: angles HIL and MLI are supplementary angles.
Hope this helps! :D
The selling price for a classic painting is $16,000, which is $2000 less than two times its original price. What was the original price of the painting?
Answer:
$9,000
Step-by-step explanation:
$16,000 + $2,000 = $18,000
$18,000/2 = $9,000
I think this is correct but I'm not sure.
Given f(x) = 2x^2 - 3 and g(x) = x + 4.
What is (f g)(x)?
Answer:
2x³+8x²-3x-12
Step-by-step explanation:
It means function f times by function g.
so fg= (2x²-3)(x+4)=2x³+8x²-3x-12
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 29 houses that sold in their neighborhood took an average time of 230 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 35 days.
a. What assumption regarding the population is necessary for making an interval estimate of the population mean?
Assume that the population has a normal distribution.
Assume that the population has a uniform distribution.
b. Construct a 90% confidence interval of the mean sale time for all homes in the neighborhood.
Answer:
a. Assume that the population has a normal distribution.
b. The 90% confidence interval of the mean sale time for all homes in the neighborhood is between 219.31 days and 240.69 days.
Step-by-step explanation:
Question a:
We have to assume normality.
Question b:
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 - 0.9}{2} = 0.05[/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 - 0.05 = 0.95[/tex], so Z = 1.645.
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 = 1.645\frac{35}{\sqrt{29}} = 10.69[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 230 - 10.69 = 219.31 days.
The upper end of the interval is the sample mean added to M. So it is 230 + 10.69 = 240.69 days.
The 90% confidence interval of the mean sale time for all homes in the neighborhood is between 219.31 days and 240.69 days.
Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is known that the standard deviation of service life for the population of white light bulbs is hours and hours for color bulbs, both are normally distributed. He tested the mean service life of those two types of bulbs by randomly drawing a sample of 20 bulbs from each type. The estimated mean service life are hours and hours. Assume that . What is the absolute value of the t-statistic if the null hypothesis is that both types of bulbs have the same service life?
Answer:
The answer is "3.51".
Step-by-step explanation:
[tex]\to t=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\sigma_x^2}{n_x}+\frac{\sigma_y^2}{n_y}}}\\\\[/tex]
[tex]=\frac{960-945}{\sqrt{\frac{14^2}{20}+\frac{13^2}{20}}}\\\\=\frac{15}{\sqrt{\frac{196}{20}+\frac{169}{20}}}\\\\=\frac{15}{\sqrt{\frac{196+169}{20}}}\\=\frac{15}{\sqrt{\frac{365}{20}}}\\\\=\frac{15}{\sqrt{18.25}}\\\\=\frac{15}{4.27}\\\\=3.51[/tex]
Jason had to determine the solution set of x squared + StartFraction y squared Over 49 EndFraction greater-than 1. Examine the graph he drew.
Which element, if any, is incorrect in the graph?
The graph is correct.
The boundary should be a solid line.
The major axis should be horizontal.
The shaded region that represents the solution set should be inside the ellipse.
ITS A:The graph is correct.
Answer:
a the graph is correct
Step-by-step explanation:
edg 21 ^u^
The graph x² + ( y²/49 )>1 is correct. The correct option is A.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given inequality is x² + ( y²/49 )>1;. The graph is plotted on the x-y plane. The curves of the graph cut the y-axis at positive 7 and negative 7 and cut the x-axis at positive 1 and negative 1.
Hence, the correct option is A.
To know more about inequality follow
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Please help!! Due in 45 minutes.
Answer:
[tex]x = \frac{56}{9} , y =-\frac{26}{3}[/tex]
Step-by-step explanation:
Calculator work :)
I need helppppppppppppppppp
Answer:
Are you giving any exam or what?
Answer:
C. 3x^2-2x=0
Step-by-step explanation:
3x^2+2x=x(3x+2)=0
x=0 or 3x+2=0⇒3x=-2⇒x=-2/3
NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER
Please solve
Step by step
How would one convert 6 lb to ounces (16 oz = 1 lb)?
O A. 6 lb
16 oz
1 lb
O B.
6 lb
16 OZ
O C. 6 lb x 16 oz
O D. 61bx
1 lb
16 oz
Answer:
6 * 16
Step-by-step explanation:
One pound is 16oz.
Multiply the number of pounds by 16.
6 * 16 = 96
6 pounds is 96oz.
Hope this helps.
Answer:6lb x 16oz/1lb
Step-by-step explanation:just took the test
sphere has a diameter of 14 ft. What is its surface area?
someone please help me answer this!!
Answer:
39
Step-by-step explanation:
You should use the pythagorean theorem!
How do you convert length to cm, in, ml etc.
Answer:
Use an online converter but there is something you should know
Step-by-step explanation:
There are two systems of measurement. The Imperial system (inch, mile, cups, ounces) and the Metric system (millimeter, centimeter, gram, kilogram).
Converting measurements in the imperial system by memory is very hard, but converting measurements in the metric system is more simple.
It is easier to learn by images so here is an image that explains it
Keep in mind that measurements like inches and centimeters are for distance, while gram and ounces are for weight.
if the game begins at 1 pm and charlie and his friends take 1.5 hours to get to the field what time should they leave
Answer:
11:30am
Step-by-step explanation:
Answer:
Charlie and his friends should leave by 11:30 am at the latest.
Help me im stuck answer a b c and d please I don't know if they right
Answer:
It’s b
Step-by-step explanation:
Morty spent $54 on tulips and roses and bought a total of 14 flowers. If tulips cost $5 and roses $3
Let t = number of tulips bought
Let r = number of roses bought
a) Write the system.
b) How many of each flower did Morty buy? (Solve the system)
Answer:
a) Let's define the variables:
t = number of tulips bought
r = number of roses bought
We know that each tulip costs $5, and each rose costs $3.
Then the total cost will be:
$5*t + $3*r
We know that Morty spent a total of $54, then we have the equation:
$5*t + $3*r = $54
We also know that he bought a total of 14 flowers, then:
r + t = 14
Then the system of equations is:
$5*t + $3*r = $54
r + t = 14
b) To solve the system, first, we need to isolate one of the variables in one of the equations. I will isolate r in the second one:
r = 14 - t
Now we can replace this into the other equation:
$5*t + $3*r = $54
$5*t + $3*(14 - t) = $54
Now we can solve this for t.
$5*t + $3*14 - $3*t = $54
$2*t + $42 = $54
$2*t = $54 - $42 = $12
t = $12/$2 = 6
t = 6
He bought 6 tulips.
Now we can use the equation r = 14 - t
r = 14 - 6 = 8
r = 8
He bought 8 roses.
A sewing machine sews at a constant rate of 1,500 stitches per minute. If the equation, y = 1,500x represents the relationship between the number of minutes, x, and the total number of stitches, y, what is the independent and dependent variable? (EE.C.9b)
Answer:
Step-by-step explanation:
x is the independent variable. y is the dependent variable.
Dependent variables take their values based on values of independent variables. In the considered case, we have:
Independent variable is x = number of minutesDependent variable is y = total number of stitchesWhat are independent and dependent variables?Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.
If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable.
The variables who take their values based on some other variables' values are called dependent variables.
For the considered case, the two variables in consideration are:
x = number of minutesy = the total number of stitchesTime doesn't depend on number of stitches. Its thus, measuring an independent quantity.
The total number of stitches depends on how much time it passed since sewing. So the quantity 'y' depends on the value of 'x'
Thus, variable 'y' is dependent variable.
Therefore, in the considered case, we have:
Independent variable is x = number of minutesDependent variable is y = total number of stitchesLearn more about dependent and independent quantities here:
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Find the value of x in the figure below if RE is parallel to PM.
2.3 units
16 units
21 units
4.6 units
Answer:
21 units
Step-by-step explanation:
Since,
RE is parallel to PM,
( AR / RP ) = ( AE / EM )
( 7 / x ) = ( 6 / 18 )
( 7 / x ) = ( 1 / 3 )
x × 1 = 7 × 3
x = 21 units
Plz help me, ASAP look at the photo
Answer:
Input Output
0 1
2 2
-8 -3
100 51
Step-by-step explanation:
Given
The rule: input ⇒ ÷2+1 ⇒ output
Solve
0 ⇒ 0÷2+1 ⇒ 1
2 ⇒ 2÷2+1 ⇒ 2
-8 ⇒ -8÷2+1 ⇒ -3
100 ⇒ 100÷2+1 ⇒ 51
Hope this helps!! :)
Please let me know if you have any questions
Preston has a car washing business. Last year he washed 20 cars a week. This year, he washed 1,200 cars. How many more cars did he wash this year than last year? *52 weeks=1 year
Answer:
160 cars
Step-by-step explanation:
The computation of the number of more cars he washed this year is given below;
Last year, he washed 20 cars a week so on yearly basis he washed
= 20 cars × 52 weeks
= 1,040 cars
And, this year he washed 1,200 cars
So, the number of more cars he washed this year is
= 1,200 cars - 1,040 cars
= 160 cars