Dell Computers receives large shipments of microprocessors (chips) from Intel Corp. It must try to ensure that the proportion of defective chips is small and has contracted to keep the proportion of defective chips at 5% or less. Suppose that Dell tests 25 chips (with replacement) out of a shipment of thousands.
a) What is the probability of obtaining at least three defects in the sample, if the entire shipment has 5% defectives? If a sample results in at least three defects, does it appear that Intel has provided a shipment which is consistent with the contract? Briefly explain, using the calculated probability.
b) For the shipment described in part a, find the expected number of sampled chips that are defective and the standard deviation of the number of sampled chips that are defective.
c) Suppose that 20% of the entire shipment is defective. What is the probability that more than 17 chips in the sample are good (not defective)?
Using the binomial distribution, it is found that:
a) 0.1271 = 12.71% probability of obtaining at least three defects in the sample, if the entire shipment has 5% defectives. 5% defective is between 1 and 2 defects, but since this probability is more than the unlikely threshold 5%, more than 2 defects could still mean that Intel has provided a shipment which is consistent with the contract.
b) The mean is of 1.25 defective chips and the standard deviation is of 1.09 defective chips.
c) 0.8908 = 89.08% probability that more than 17 chips in the sample are good.
For each chip, there are only two possible outcomes, either it is defective, or it is not. The probability of a chip being defective is independent of any other chip, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
25 chips are tested, thus, [tex]n = 25[/tex].Item a:
Supposing 5% defective, we have that [tex]p = 0.05[/tex].
The probability is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{25,0}.(0.05)^{0}.(0.95)^{25} = 0.2774[/tex]
[tex]P(X = 1) = C_{25,1}.(0.05)^{1}.(0.95)^{24} = 0.3650[/tex]
[tex]P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2774 + 0.3650 + 0.2305 = 0.8729[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8729 = 0.1271[/tex]
0.1271 = 12.71% probability of obtaining at least three defects in the sample, if the entire shipment has 5% defectives. 5% defective is between 1 and 2 defects, but since this probability is more than the unlikely threshold 5%, more than 2 defects could still mean that Intel has provided a shipment which is consistent with the contract.
Item b:
The mean is:
[tex]E(X) = np = 25(0.05) = 1.25[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{25(0.05)(0.95)} = 1.09[/tex]
The mean is of 1.25 defective chips and the standard deviation is of 1.09 defective chips.
Item c:
20% are defective, so 80% are good, which means that [tex]p = 0.8[/tex]
The probability is:
[tex]P(X > 17) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 18) = C_{25,18}.(0.8)^{18}.(0.2)^{7} = 0.1108[/tex]
[tex]P(X = 19) = C_{25,19}.(0.8)^{19}.(0.2)^{6} = 0.1633[/tex]
[tex]P(X = 20) = C_{25,20}.(0.8)^{20}.(0.2)^{5} = 0.1960[/tex]
[tex]P(X = 21) = C_{25,21}.(0.8)^{21}.(0.2)^{4} = 0.1867[/tex]
[tex]P(X = 22) = C_{25,22}.(0.8)^{22}.(0.2)^{3} = 0.1358[/tex]
[tex]P(X = 23) = C_{25,23}.(0.8)^{23}.(0.2)^{2} = 0.0708[/tex]
[tex]P(X = 24) = C_{25,24}.(0.8)^{24}.(0.2)^{1} = 0.0236[/tex]
[tex]P(X = 25) = C_{25,25}.(0.8)^{25}.(0.2)^{0} = 0.0038[/tex]
Then:
[tex]P(X > 17) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.1108 + 0.1633 + 0.1960 + 0.1867 + 0.1358 + 0.0708 + 0.0236 + 0.0038 = 0.8908[/tex]
0.8908 = 89.08% probability that more than 17 chips in the sample are good.
A similar problem is given at https://brainly.com/question/24863377
The equation
(p-1)x^2 + 4x + (p-5)=0, where p is a constant,
has no real roots.
(a) Show that p satisfies p^2 - 6p+1>0.
Answer:
Proof is shown below.
Step-by-step explanation:
Use quadratic Formula, where from the standard form ax^2 + bx + c = 0, where a is not zero, we identify a = p-1, b=4, c = p-5, and since the given equation has no real roots, the discriminant b^2 - 4ac < 0, so that substituting we have that,
4^2 - 4(p-1)(p-5) < 0
16 - 4(p^2 - 6p + 5) < 0
16 - 4p^2 +24p - 20 < 0
-4p^2 + 24p - 4 < 0,
p^2 - 6p + 1 > 0, by dividing both sides of the inequality by -4.
Lillie is saving up for a trip she is taking with friends during her break from school. If Lillie's current monthly net pay is $429.00 and her monthly expenses are $347.49, what percent of her net pay is left for savings?
a
19%
b
23%
c
65%
d
81%
solve pls brainliest
Answer:
1) 2
2) 1
3) 8
Step-by-step explanation:
brainliest plz
50×54+35-44
Simplification
no spam
steps must
Answer:
=2691
Step-by-step explanation:
=2700+35−44
=2735−44
=2691
Suppose there is a 1.2 drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 57.8, what will be the temperature when the plane reaches an altitude of 7000?
Answer:
ysgsvdbdbdjdnd dndjdnd
Trong 300 người bệnh chỉ dùng thuốc A có 55% người khỏi; trong 240 người bệnh chỉ dùng thuốc B có 50% người khỏi. Với mức ý nghĩa 5% có thể nói thuốc A hiệu quả hơn thuốc B không?
vâng vì phụ nữ là những người tán gẫu
direct variation
Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. if a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?
pls help (;ŏ﹏ŏ)
When a force of 270N is applied, the spring stretch by 7.5cm
Two variables are said to be directly proportional if as one variable increases/decreases, the other variables does the same by the same amount.
Let F represent the force and x represent the extension, hence:
F ∝ x
F = kx; k is the constant of proportionality
When F = 180, x = 5, hence:
180 = 5k
k = 36
F = 36x
When F = 270:
270 = 36x
x = 7.5 cm
When a force of 270N is applied, the spring stretch by 7.5cm
Find out more at: https://brainly.com/question/13977805
Noah bought 15 baseball cards for $9.00 assuming each baseball card cost the same amount answer the following questions
Answer:
Well, each baseball card $1.60.
Step-by-step explanation:
Since, you may just divide the amount of cards to the amount of money required.
Three workers worked for 5 hours, 7 hours and 12 hours. The total wage of $
13200 was divided among the three workers according to the number of hours of
work they did. How much did each get?
Answer:
Worked 5 hours: $550
Worked 7 hours: $2,750
Worked 12 hours: $6,600
Step-by-step explanation:
5+7+12=24
13200/24 = 550
(5)*(550) = 2,750
(7)*(550) = 3,850
(12)*(550) = 6,600
If a square has a perimeter of 36cm how long is each side of the square
Answer:
9 cm
Step-by-step explanation:
→ Remember how many sides a square has
4
→ Divide it by the perimeter
36 ÷ 4 = 9
Step-by-step explanation:
you know what a square is ?
it is a closed shape with 4 sides.
all 4 sides are equally long.
all 4 inner angle are 90 degrees.
you know what a perimeter is ?
it is the circumference, the whole way one time around the shape, around the outline of a given structure.
if you don't know the terms, for heaven's sake, please ask your teacher, your friends, your parents or us here directly.
don't wait. don't be afraid or ashamed.
because this here is an extremely simple problem to solve, once you understand the words used.
so, as per the explanations, the perimeter of a square is the sum of the lengths of all sides. and because all sides are equally long, this means the perimeter is simply 4 times the length of one side.
36 = 4×side
side = 36/4 = 9cm
so, each side of the square is 9cm long.
I need help answering this question please
help me with this question please!!
Answer:
A = 2 pi R^2 + 2 pi R h total surface area
R^2 = 48 2 pi R = 8 * 6^1.2 given
56 pi 6^1/2 - 2 pi R^2 = 2 pi R h f rom first formula
28 * 6^1/2 / R - R = h divide by 2 pi r
28 * 6^1/2 / R = 28 * 6^1/2 / (4 3^1/2) = 7 * 2^1/2
h = 7 * 2^1/2 - 4 * 3^1/2
Wooden flooring costs £35 per square metre. The floor is then edged with a narrow wooden strip which costs £4 per metre.
How much does it cost for a 6m by 4m room, including the edging?
Answer:
£920
Step-by-step explanation:
We need to find the area of floor to find the cost of the flooring, and then we need to find the perimeter of the floor to find the cost of the edging.
A = LW = 6 m × 4 m = 24 m²
Cost of flooring: 24 m² × £35/m² = £840
P = 2(L + W) = 2(6 m + 4m) = 2(10m) = 20 m
Cost of edging: 20 m × £4/m = £80
Total cost:
£840 + £80 = £920
Write the equation of the line, given the y and x-intercepts. a x-intercept = –68, y-intercept = –34
Answer:
In slope-intercept form, y = -17/34 - 34
Step-by-step explanation:
For the two points, you have (-68, 0) and (0, -34). To get the slope, you take (y-y) / (x-x). Stay consistent on the order you do those. After I did (-34 - 0) / (0 - 68), simplified it, and got a slope of -17 / 34. You are already given the y-intercept, so you just write the equation from there (y = -17/34 - 34)
2. Louis kept losing money through a hole in his pocket. He started with 35€, lost 20€.
put in 754 more, spent 43¢ lost 16¢ again, and then put in 14¢. How much change should
there be in his pocket?
Your answer should be 724 cents, in dollars that is $7.24
Step-by-step explanation:
from the cents is shoes be 724 and the dollars souls be $7.24
b. What is the number that is halfway between the two values?
7 and 11
Submit
Answer:
9
Step-by-step explanation:
It would be 9 because 7 +2 is 9 and 11 - 2 is 9.
Isn't way to hard.
Good luck on whatever you are doing.
9514 1404 393
Answer:
9
Step-by-step explanation:
The midpoint between two values is their average. The average is half their sum.
(7 +11)/2 = 18/2 = 9
The number 9 is halfway between 7 and 11.
_____
Check
The distance from 7 to 9 is 9-7 = 2. The distance from 9 to 11 is 11-9 = 2. The distances are the same, so 9 is halfway between 7 and 11.
covert 31 days into minutes
Answer:
MARK ME AS BRAINLIEST !!
Step-by-step explanation:
44640
Answer:
31 days =
44640 minutes
Step-by-step explanation:
Welcome
Find the Value of x
Please answer!!
No links!!
Answer:
x = 15 inches
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\b^{2} = c^{2} - a^{2} \\b^{2} = (25 inches)^{2} - (40 inces/2)^{2} = \sqrt{225} = 15 inches[/tex]
150 miles on 4 gallons of gas. How many miles for 1 gallon of gas?
Answer: answered
A motorcycle can go 50 miles using one gallon of gas. About how many gallons of gas will be used to go 150 kilometers? (Hint: 1 mile is approximately 1.6 kilometers)
Step-by-step explanation:
Answer:37.5
Step-by-step explanation:
7. The ratio of the base to height of a triangle is 3:5. If the area of this triangle is 30, find the lengths of the base and height.
Answer:
Base= 6
Height= 10
Step-by-step explanation:
Area of triangle= ½ ×base ×height
Let the base be 3x and the height be 5x.
Given that the area is 30,
½ ×base ×height= 30
½(3x)(5x)= 30
Multiply both sides by 2:
3x(5x)= 60
15x²= 60
x²= 60 ÷15
x²= 4
Square root both sides:
[tex]x = \sqrt{4} [/tex]
x= 2
(reject x= -2 since length has a positive value)
Length of base
= 3x
= 3(2)
= 6
Length of height
= 5x
= 5(2)
= 10
I have more questions to due after this
Answer:
a reflection over the line y=-x
Step-by-step explanation:
ReWrite 2/3 and 3/4 with a common denominator
Answer:
8/12 and 9/12
Step-by-step explanation:
Find the slope between these two points:
(4,7).(-6, -4)
Answer:
1.1
Step-by-step explanation:
slope = (-4-7)/(-6-4)= -11/-10 = 1.1
QUICK!!
fill in the blanks below in order to justify whether or not the mapping shown represents a function.
Step-by-step explanation:
I don't know what the specific options are to be selected, but I can tell you what the situation is, and you can then pick the fitting options on your screen :
it is not a function, because 5 in set A (the domain) leads to 2 associated (functional result) values in B (the range).
but in order to be a function, every input value must have exactly one resulting output value. which is violated here.
A salesperson earns an income of $600 per week aus an dditional 5% commission on her total sales for that weck a. Write an equation that models the Salespersons total weekly income. b. What would be the salespersons income if her total sales were $10.000 that week? c. How much would a salesperson have to sell to have a $2000 weekly
help me out with this problem ?
Answer:
(-4.5, 2.5)
Step-by-step explanation:
The solution for two graphed linear equations is the intersection (The point where two lines meet or cross).
The lengths of the worms (in inches) are listed here.
Which line plot shows this data?
Answer:
Top Left
Step-by-step explanation:
The numbers all coordinate to that plot
Answer:
Plot #1Step-by-step explanation:
The easy way is to look for exceptions. The first and last plots missing 7/8 and same with data set.
There are 4 1's in the set which is correct with the first plot.
[tex]\frac { a } { ( a - b ) ( a - c ) } + \frac { b } { ( b - c ) ( b - a ) } + \frac { c } { ( c - a ) ( c - b ) }[/tex]
the formula is the question pleaseee helppp quickkk
Answer:
0
Step-by-step explanation:
[tex]\frac{a}{(a-b)(a-c)} +\frac{b}{(b-c)(b-a)}+\frac{c}{(c-a)(c-b)}\\= \frac{a}{(a-b)(a-c)} -\frac{b}{(b-c)(a-b)}+\frac{c}{(a-c)(b-c)}\\\\= \frac{a(b-c)-b(a-c)+c(a-b)}{(a-b)(a-c)(b-c)}}\\\\= \frac{ab-ac-ab+bc+ac-bc}{(a-b)(a-c)(b-c)}}\\\\= \frac{0}{(a-b)(a-c)(b-c)}}\\\\= 0[/tex]
Andre wrote the expression -2 + 4x = 3 to represent the relationship shown in the table. Write two other expressions that also represent the relationship shown in the table.
Two other expressions that also represent the relationship shown in the table are;
4x-5 = 04x-5 = 0x = 5/4According to the question;
Andre wrote the expression -2 + 4x = 3 to represent the relationship shown in the tableIn essence, to write two other expressions that also represent the relationship shown in the table; we can rearrange the terms in the expression Andre wrote (-2 + 4x = 3) as follow;
First expression is;
-2 - 3 + 4x = 04x-5 = 0Second expression is;
4x = 5x = 5/4Read more:
https://brainly.com/question/13968118