1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
o-na [289]
2 years ago
12

Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X deno

te the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more than 3 standard deviations.
a. If the percentage of parts that require rework remains at 1%, what is the probability that X exceeds its mean by more than 3 standard deviations?
b. If the rework percentage increases to 4%, what is the probability that X exceeds 1?
c. If the rework percentage increases to 4%, what is the probability that X exceeds 1 in at least one of the next five hours of samples?
Mathematics
1 answer:
Roman55 [17]2 years ago
3 0

Answer:

a) P(X>np+3\sqrt{np(1-p)}=0.017

b) P(x>1)=0.190

c) P(Y>1)=0.651

Step-by-step explanation:

This a binomial experiment where success is denoted by parts that need rework.

X ∼ B(n, p); n = 20; p = 0.01

The expected value of X is: E(X) = np =20×0.01= 0.2

The variance is: Var(X) = np(1 − p) = 0.2 × 0.99 = 0.198,

The standard deviation SD(X)= \sqrt{0.198} ≈ 0.445

a) P(X>np+3\sqrt{np(1-p)}=P(X>0.2+3×0.445)=P(X>1.535)=P(X≥2)

Probability function is given by:

\frac{n!}{x!(n-x)!} *p^x*(1-p)^{(n-x)}

P(X≥2)=1-P(X<2)=1-P(X=1)-P(X=0)= 1 - \frac{20!}{1!(20-1)!} *(0.01)^{1}*(1-0.01)^{(20-1)}-\frac{20!}{0!(20-0)!} *(0.01)^{0}*(1-0.01)^{(20-0)}

P(X≥2)=1-0.165-0.818=0.017

b) p=0.04

P(x>1)=P(x≥2)= 1 - P(x=1) - P(x=0)= 1 - \frac{20!}{0!(20-1)!} *(0.04)^{1}*(1-0.04)^{(20-1)} - \frac{20!}{0!(20-0)!} *(0.04)^{0}*(1-0.04)^{(20-0)}

P(x>1)= 1 - 0.368 - 0.442=0.190

c) In this case we consider p=0.19 (Probability that X exceeds 1)

In this experiment Y is the number of hours and n= 5 hours.

Then, we check the probability in each hour:

P(Y>1)=1- P(Y=0)

P(Y=0)=\frac{5!}{0!(5-0)!} *(0.19)^{0}*(1-0.19)^{(5-0)}=0.349

P(Y>1)=1-0.349=0.651

You might be interested in
Prove that if a, b ∈ n, then the supremum i.e. the least upper bound of {a, b} is the lcm(a, b).
WINSTONCH [101]
─────█─▄▀█──█▀▄─█─────
────▐▌──────────▐▌────
────█▌▀▄──▄▄──▄▀▐█────
───▐██──▀▀──▀▀──██▌───
──▄████▄──▐▌──▄████▄──
6 0
3 years ago
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = -2. The y-intercept
Maru [420]

Answer:

p(x) =  - 0.7(x - 3)^{2} (x + 2)

Step-by-step explanation:

We have that the polynomial, has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = -2.

This means the factored form of the polynomial will be.

p(x) = a(x - 3)^{2} (x + 2)

Also, it was given that, the y-intercept is y=-12.6.

This implies that:

- 12.6= a(0 - 3)^{2} (0 + 2)

- 12.6= a(- 3)^{2} (2)

- 12.6= 18a

Divide both sides by 18;

a =  \frac{ - 12.6}{18}

a= - 0.7

Therefore the polynomial is

p(x) =  - 0.7(x - 3)^{2} (x + 2)

7 0
3 years ago
A waether forecast predicts a 30% chance of rain for each of the next 3 days. Describe a way to stimulate the chance that it wil
DerKrebs [107]
Using a binomial distribution considering there's a 30% chance it will rain on any of the three days: 

<span>The probability of it raining on 0 days is (1)(0.7)(0.7)(0.7) = 34.3%. </span>
<span>The probability of it raining on 1 day is (3)(0.3)(0.7)(0.7) = 44.1%. </span>
<span>The probability of it raining on 2 days is (3)(0.3)(0.3)(0.7) = 18.9%. </span>
<span>The probability of it raining on 3 days is (1)(0.3)(0.3)(0.3) = 2.7%. </span>

<span>There's a 65.7% chance that it will rain at least once over the three-day period.</span>
5 0
3 years ago
The equation of a line is y = 12x - 3. Write the equation of a line parallel to this line.
VladimirAG [237]

Answer:

y=12x+3

Step-by-step explanation:

when parallel the slopes need to be the same but the y-intercept has to change

8 0
2 years ago
Người ta thống kê được rằng mỗi chuyến bay có chừng 0,5% hành khách bị mất hành lí và giá trị trung bình mà khách đòi bồi thường
Butoxors [25]

Answer:

tăng lên 5.000 nghìn đồng

Step-by-step explanation:

mỗi chuyến bay có 0.5% hành khách mất hành lí

mỗi người đòi bồi thường 1.000.000 đồng

do đó vẽ mỗi người tăng lên :0.5%×1.000.000=5.000

5 0
3 years ago
Other questions:
  • The difference between thirteen and the product of four and a number? in algrebrain expression
    8·2 answers
  • A store sells 8 cans of nuts for $18. how much would it cost to buy 3 cans of nuts
    13·2 answers
  • A number has a 5 in the tens place. The number of ones is 3 less than the number of tens. The number of hundreds is 1 less than
    6·1 answer
  • Solve the system of equation by graphing
    9·1 answer
  • what is the probability that a red or green marble will be selected from a bag containing 9 red marbles, 7 green marbles, and 11
    7·1 answer
  • Sam ran 63,756 feet in 7 hours. what is sam's miles per hour
    15·2 answers
  • HELP ME PLEASE!! A total of 30 shirts were sold at Friday night's football game. Each adult shirt cost $10.50 and each youth shi
    5·1 answer
  • Keep that Michelle went out To dinner. The total cost of the meal, including the tip, came out to $53.70. It's a combined tip ca
    11·1 answer
  • The ratio of pears to green apples is 1:3 if there are 150 green apples how many pears are there​
    15·2 answers
  • An electrician completes 1/6 of a job in 2/3 hour. at this rate, how long does it take the electrician to complete the job?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!