Answer:
5
Step-by-step explanation:
In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings. a. What is the probability that a given shipment is acceptable? b. What is the probability that more than 285 out of 300 shipments are acceptable? c. What proportion of bearings must meet the specification in order that 99% of the shipments are acceptable?
Answer:
(a) 0.94
(b) 0.20
(c) 90.53%
Step-by-step explanation:
From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let [tex]p_1[/tex] be the probability that a bearing meets the specification.
So, [tex]p_1=0.9[/tex]
Sample size, [tex]n_1=500[/tex], is large.
Let X represent the number of acceptable bearing.
Convert this to a normal distribution,
Mean: [tex]\mu_1=n_1p_1=500\times0.9=450[/tex]
Variance: [tex]\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45[/tex]
[tex]\Rightarrow \sigma_1 =\sqrt{45}=6.71[/tex]
(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.
So, [tex]X\geq 440.[/tex]
Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.
[tex]z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56[/tex].
So, the probability that a given shipment is acceptable is
[tex]P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062[/tex]
Hence, the probability that a given shipment is acceptable is 0.94.
(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.
Denote the probability od acceptance of a shipment by [tex]p_2[/tex].
[tex]p_2=0.94[/tex]
The total number of shipment, i.e sample size, [tex]n_2= 300[/tex]
Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, [tex]\mu_2[/tex], and variance, [tex]\sigma_2^2[/tex].
Mean: [tex]\mu_2=n_2p_2=300\times0.94=282[/tex]
Variance: [tex]\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92[/tex]
[tex]\Rightarrow \sigma_2=\sqrt(16.92}=4.11[/tex].
In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.
[tex]z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85[/tex].
So, the probability that a given shipment is acceptable is
[tex]P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977[/tex]
Hence, the probability that a given shipment is acceptable is 0.20.
(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).
The area right to the z-score=0.99
and the area left to the z-score is 1-0.99=0.001.
For this value, the value of z-score is -3.09 (from the z-score table)
Let, [tex]\alpha[/tex] be the required probability of acceptance of one shipment.
So,
[tex]-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}[/tex]
On solving
[tex]\alpha= 0.977896[/tex]
Again, the probability of acceptance of one shipment, [tex]\alpha[/tex], depends on the probability of meeting the thickness specification of one bearing.
For this case,
The area right to the z-score=0.97790
and the area left to the z-score is 1-0.97790=0.0221.
The value of z-score is -2.01 (from the z-score table)
Let [tex]p[/tex] be the probability that one bearing meets the specification. So
[tex]-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}[/tex]
On solving
[tex]p=0.9053[/tex]
Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.
The manufactures bearings.
As per the question, the process that a manufacturer bears 90% of the bearings and meet the thickness specifications. The shipment consists of 500 bearings. The shipment if taken has a least 440 and 500 bearings.
the answer is 0.94, 0.20, and 90.53%.
The assumption is that each shipment is randomly taken in a sample of bearings. The chances or the probability that that given shipment are acceptable are 0.94% and the probability that they are more than 285 out of the 300 bearings is 0.205. The part of bearings that must meet the specifications in order to be 99% of shipments is 90.5%.Learn more about the manufactures bearings.
brainly.com/question/15686369.
Is thirty six and nine thousandths greater or less than 4 tens
Greater
36+9,000 > 40
What’s the range? 10 points ! !
Answer:
[-7,2]
Step-by-step explanation:
the range is all the possible y-values, and the highest point of the graph is at (-3,2) while the lowest is at (0,-7). when looking at the y-coordinates, we realize that the range is [-7,2] (brackets because those points are included).
Casey did a science experiment to find out which brand of popcorn popped the most kernels. The first brand had 123 kernels pop. The second brand had 108 kernels pop. To the nearest ten, about how many kernels popped in all?
Answer:
230
Step-by-step explanation:
The answer is 230 because if you add 123 and 108 together you get 231 but since we are rounding to the nearest 10 it would be 230 because 231 is closer to 230 than it is to 240.
Classwork
1. A plane flew at a constant speed between Denver and Chicago. It took the
plane 1.5 hours to fly 915 miles. Complete the table.
Time in Hours (x)
Distance in Miles (y)
Constant (3)
1
1.5
915
2
2.5
Hint - Find the constant of proportionality first (y/x=k).
Answer:
Time in hours (x) ==> distance in miles (y)
1 ==> 610
2 ==> 1,220
2.5 ==> 1,525
Note: constant of proportionality is same all through = 610
Step-by-step explanation:
Constant of proportionality = [tex] \frac{y}{x} = \frac{915}{1.5} = 610 [/tex]
To get the y-values (miles) for each given x-value (hours), multiply each x-value by the constant of proportionality, 610. Constant of proportionality is same all through.
Thus,
Time in hours (x) ==> distance in miles (y)
1 ==> 1*610 = 610
2 ==> 2*610 = 1,220
2.5 ==> 2.5*610 = 1,525
Someone please help. If you don’t want to answer all that’s fine
Answer:
1. ) Plane ABC
2.) Segment AD
3.) Segment DE
4.) Segment AC
I'm sorry I don't know how to complete the 2nd half, but I hope these help. :)
The race course is 3/4 of a mile long. How many feet long is the race course?
Answer:
3960 feet
Step-by-step explanation:
Answer:
3,960 feet long
Step-by-step explanation:
1 mile = 5,280 feet
5,280 feet ÷ 4 (because the denominator is 4) = 1,320 feet
1,320 x 3 (the numerator is 3) = 3,960 feet
3/4 of a mile = 3,960 feet
one third of a number is greater than one tenth of that same number by 63 what is the number
Answer:
The answer is 270.
Step-by-step explanation:
This is the answer is because:
If you let the number be x.
x divided by 3 is equal to x divided by 10 plus 63.
x/3 = x/10 +63
So...
x divided by 3 plus x divided by 10 is equal to 63
x/3 +x/10 = 63
Then if you make a commmon denominator...
10x divided 30 plus 3x divided by 30 is equal to 63
10x/30 + 3x/30 = 63
Then...
7x divided by 30 is equal to 63
7x/30 = 63
After that...
x is equal to ( 63 * 30 ) divided by 7
x = (63*30) / 7
So...
x is equal to 9*30
x = 9*30
Finally...
x is equal to 270
x = 270
The product of -9 and a number, increased by 15 is -7. Find the number.
Answer: the answer is -23 i think
Step-by-step explanation:
g(n)=n+1 f(n)-n^2-n find g(f(8))
Step-by-step explanation:
[tex]g(f(8)) =( n ^{2} - n )+ 1 = 8 ^{2} - 8 + 1 = 64 + 9 = 73[/tex]
Can someone please help me!!
Find the common ratio of the geometric sequence –4, 32, —256, ...
Answer: -8
Step-by-step explanation:
R= a2/a1
32/-4 divide by 4 to simplify so its -8
-4*-8= 32
32*-8 = -256
What is the result of 5 divided by 1/5?
Answer:
15 divided by 1/5 is equal to 1.
how can I solve this equation
49x^2 - 14x + 1 <= 0
Step-by-step explanation:
(7x)^2 - 2×7x×1 +1^2 =0
(7x-1)^2 =0
7x-1=0
7x=1
x= 1\7
cara is making a beaded necklace for a gift. she wants to spend more than $25 because she doesn´t want to seem like a cheap friend but no more than $60 because she isn´t that good of a friend either.the bead store charges $3 for large beads and $2 for small beads.if she buys 5 large beads, how many small beads can she buy to stay within her budget.
Answer:
5 small beads!
Step-by-step explanation:
Hey there!
If large beads are $3 each, and she buys 5 of them, our equation is $3 x 5 which equals $15. So Cara will spend $15 buying large beads.
Cara has $10 left now, because $25 - $15 = $10. Since each small bead is $2, we divide $10 (the total amount of money she has) by $2 (the cost of each bead). This will tell us how many she can buy! So $10 ÷ $2 is 5. Cara can buy 5 small beads!
I hope this helped you! Rating my answer and giving it a Thanks would sure help me out!
Have a wonderful day!
7g:1kg to its simplest form
Answer:
7kg:1kg=7:1 itself
Because 7 and 1 has one '1' as a common factor, so they can't be simplified
48% = 48 Over 100 = A Over 25. What is A?
9514 1404 393
Answer:
A = 12
Step-by-step explanation:
[tex]48\%=\dfrac{48}{100}=\dfrac{4\cdot12}{4\cdot25}=\boxed{\dfrac{12}{25}}[/tex]
Comparing this to A/25, we see that A = 12.
1/6 times 3/5 in simplist form
Answer:
0.1
Step-by-step explanation:
Subtract.
3.5 – (-6.5)
how can i show my work ?
What is the perimeter of the shape below, given a = 8.16, b = 234, C = 461,0 =
2.56, e = 8.00, f = 2.51, g = 9.81
Answer: It’s unfinded
Step-by-step explanation:
Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = p(1 - p)n-1 (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1) = 0.740 P(2) = 0.192 P(3) = 0.050 (c) Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.018 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents
Answer:
(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.
(c) The probability that n ≥ 4 is 0.018.
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.
Step-by-step explanation:
We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.
Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,
Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
So, the probability distribution of the geometric distribution is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
where, p = probability that the residents are of Hawaiian ancestry = 74%
(b) The probabilities that n = 1, n = 2, and n = 3 is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]
P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74
P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192
P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050
(c) The probability that n ≥ 4 is given by = P(n ≥ 4)
P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)
= 1 - 0.74 - 0.192 - 0.050
= 0.018
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)
We know that the mean of the geometric distribution is given by;
Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]
= [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).
geometry, please help
Answer:
I believe that number 7 is true.
Step-by-step explanation:
8. Is not a vertical angle because 3 and 3 do not look the same. The line is clearly gone on one side.
9. Is also wrong because both angles do not make a 90 degree angle.
10. Is wrong because both angles make a 90 degree angle when it should make a be 180 degrees.
( I'm learning this subject right now so it might be wrong. Tell me if I go this right.)
Container R holds a solution that is 20% alcohol and Container S holds a solution that is 60% alcohol. How many liters of solution from each container should be used to create 2 liters of solution that is 50% alcohol?
*make two equations*
Answer:
The number of liters for container R = x = 0.5 liters
The number of liters for container S = y = 1.5 liters.
Step-by-step explanation:
Let the number of liters of container R = x
Let the number of liters of container S = y
We are told in the question : that
Container R holds a solution that is 20% alcohol
= 20% × x = 0.20x
Container S holds a solution that is 60% alcohol.
= 60% × y = 0.60y
How many liters of solution from each container should be used to create 2 liters of solution that is 50% alcohol?
Hence;
x + y = 2 ....... Equation 1
x = 2 - y
0.20x + 0.60y = 2 × 50%
0.20x + 0.60y = 1........ Equation 2
Substitute
2-y for x in Equation 3
0.20(2 - y) + 0.60y = 1
0.40 - 0.20y + 0.60y = 1
Collect like terms
0.40y = 1 - 0.40
0.40y = 0.60
y = 0.60/0.40
y = 1.5 liters
Note that :
x = 2 - y
x = 2 - 1.5
x = 0.5 liters
Therefore,
the number of liters for container R = x = 0.5 liters
the number of liters for container S = y = 1.5 liters.
PLEASE HELP WILL MARK BRAINLEIST!
Answer:
-3.25
Step-by-step explanation:
Solve the equation
3m=2(4+t) for t
Which expression has the same value as9
- (-3)?
A 9 + 3
C9+(-3)
B-9+(-3)
D 9-(-3)
What is the equation of the line graphed below?
Question
The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1,4) and
B(4,1). Find the equation of the line that contains the given segment.
The line segment is AB.
The equation Is y -
Kendra is participating in a fundraiser walk-a-thon she walks 4 miles in 60 minutes how many minutes will it take to walk 7 miles
Answer:
105 min
Step-by-step explanation:
60 minutes ÷ 4 miles= 15 minutes per mile
15min per mile x 7 miles = 105 minutes
PLEASE HELP IM BEGGING YOU!!
FIND THE VALUE OF X
Answer:
12
Step-by-step explanation:
if 8+15 is about the length of the circle, the length is about 23
so 23 - 10 = 13 and the closest number to 13 is 12 so 12 is the answer
WILL GIVE BRAINLIST SO PLZ HELP
At midnight, the temperature was . At noon, the temperature was . Which expression represents the increase in temperature?
A. - 8 - 23
B. | - 8 | - 23
C. - 8 - | 23 |
D. | - 8 - 23 |
Hello!
D Would be your answer! Because At Midnight, the temperature was -8*f. At noon, 23*F, so
|-8-23| |-3||= 31 There you go! May I have Brainliest?