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
lorasvet [3.4K]
2 years ago
14

2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation

0.1. An item is considered to be defective if its weight is less than 9.8 pounds or greater than 10.2 pounds. Suppose that these items are currently produced in batches of 1000 units. a.Find the probability that at most 5% of the items in a given batch will be defective b.Find the probability that at least 85% of these items in a given batch will be acceptable.
Mathematics
1 answer:
Vesna [10]2 years ago
6 0

Answer:

Step-by-step explanation:

Given that:

population mean = 10

standard deviation = 0.1

sample mean = 9.8 < x > 10.2

The z score can be computed as:

z = \dfrac{\bar x - \mu}{\sigma}

if x > 10.2

z = \dfrac{10.2- 10}{0.1}

z = \dfrac{0.2}{0.1}

z = 2

If x < 9.8

z = \dfrac{9.8- 10}{0.1}

z = \dfrac{-0.2}{0.1}

z = -2

The p-value = P (z ≤ 2) + P (z ≥ 2)

The p-value = P (z ≤ 2) + ( 1 -  P (z ≥ 2)

p-value = 0.022750 +(1 -   0.97725)

p-value = 0.022750 +  0.022750

p-value = 0.0455

Therefore; the probability of defectives  = 4.55%

the probability of acceptable = 1 - the probability of defectives

the probability of acceptable = 1 - 0.0455

the probability of acceptable = 0.9545

the probability of acceptable = 95.45%

4.55% are defective or 95.45% is acceptable.

sampling distribution of proportions:

sample size n=1000

p = 0.0455

The z - score for this distribution at most 5% of the items is;

z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}

z = 0.6828

The p-value = P(z ≤ 0.6828)

From the z tables

p-value = 0.7526

Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526

The z - score for this distribution for at least 85% of the items is;

z = \dfrac{0.85 - 0.9545}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{-0.1045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = −15.86

p-value = P(z ≥  -15.86)

p-value = 1 - P(z <  -15.86)

p-value = 1 - 0

p-value = 1

Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1

You might be interested in
jacks mom purchased a savings bond for jack. the value of the savings bond increases by 5% each year. one year after it was purc
aalyn [17]

Answer:

Step-by-step explanation:

4 0
3 years ago
4^2 x 2<br> Please will give brainliests
vitfil [10]
4^2 = 16
16 x 2 = 32
32, Hope this helps!
4 0
3 years ago
Read 2 more answers
Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a buildi
Strike441 [17]
The range of communication is about 55 meters.
6 0
3 years ago
Mr. Richards purchased 8 T-shirts for the volleyball team. The total cost of the T-shirts was $70.56. How much did each shirt co
bezimeni [28]

Answer:

$8.82

Step-by-step explanation:

$70.56÷8 =$8.82 total

7 0
3 years ago
How to find the shaded area
tresset_1 [31]

Answer:

Step-by-step explanation:

You have to multiply

3 0
3 years ago
Other questions:
  • 25 POINTS!!!!!!!!!!!!
    6·1 answer
  • How do you do this question
    5·1 answer
  • Write 5x - 15y = -8 in slope-intercept form
    10·2 answers
  • Find the value of x in each figure. help
    8·1 answer
  • Christopher has 3/4 of a pie . Alex has 2/3 of a pie. Jaden has 1/2of a pie. Who has the biggest amount? Who has the least? How
    13·1 answer
  • What is 69510 over 22 as a decimal
    9·1 answer
  • 12. Phil invests $5000 in a high-interest savings account and earns 3.5% simple
    12·1 answer
  • What is 3.4/2.24 equal to? The four possible answers are 340/224, 34/224, 34/2.24, and 3.4/224 which one is correct
    13·1 answer
  • 60 minutes = to how many hours​
    6·1 answer
  • An arc subtends a central angle measuring \dfrac{7\pi}{4}
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!