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
Vera_Pavlovna [14]
3 years ago
5

Automated manufacturing operations are quite precise but still vary, often with distribution that are close to Normal. The width

in inches of slots cut by a milling machine follows approximately the N(0.72,0.0012) distribution. The specifications allow slot widths between 0.71975 and 0.72025. What proportion of slots meet these specifications
Mathematics
1 answer:
konstantin123 [22]3 years ago
4 0

Answer:

The proportion of slots which meet these specifications is 0.16634 or 16.63%.

Step-by-step explanation:

We are given that the width in inches of slots cut by a milling machine follows approximately the N(0.72,0.0012) distribution.

Also, the specifications allow slot widths between 0.71975 and 0.72025.

<u><em>Let X = width in inches of slots cut by a milling machine </em></u>

The z-score probability distribution for normal distribution is given by;

                           Z = \frac{  X-\mu}{{\sigma}} }} } ~ N(0,1)

where, \mu = population mean width = 0.72

            \sigma = standard deviation = 0.0012

           

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the specifications allow slot widths between 0.71975 and 0.72025 is given by = P(0.71975 < X < 0.72025)

      P(0.71975 < X < 0.72025)  = P(X < 0.72025) - P(X \leq 0.71975)

     P(X < 0.72025) = P( \frac{  X-\mu}{{\sigma}} }} } < \frac{ 0.72025-0.72}{{0.0012}} }} } ) = P(Z < 0.21) = 0.58317

     P(X \leq 0.71975) = P( \frac{  X-\mu}{{\sigma}} }} } \leq \frac{ 0.71975-0.72}{{0.0012}} }} } ) = P(Z \leq -0.21) = 1 - P(Z < 0.21)

                                                                    = 1 - 0.58317 = 0.41683

<em>So, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.21 in the z table which has an area of 0.58317.</em>

Therefore, <em> </em>P(0.71975 < X < 0.72025)  = 0.58317 - 0.41683 = <u>0.16634</u>

Hence, the proportion of slots who meet these specifications is 16.63%.

You might be interested in
Solve 2 1/4 + 6% = 6% -4%​
Novay_Z [31]

Answer:

God will help you and has a plan for you. Please don't cheat or look up answers. I used to be like you but I stopped. God always has a plan for you! Just remember this. He loves you. Share the message

Step-by-step explanation:

3 0
2 years ago
12k+5=k+49 what's the answer
dybincka [34]
The answer is k=4 you're welcome
3 0
3 years ago
Pls help I will mark brailiest​
Elena L [17]

Answer:

c,d,e

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
9. What is the distance along the x axis from order pairs -8, 6 and 4,6
Blababa [14]

Answer:

12 units

Step-by-step explanation:

got it right on edg

5 0
3 years ago
Solving right triangles
ratelena [41]
All you need is use sin cos tan for doing this
sin (angle)= O/H
cos (angle)= A/H
tan (angle)= O/A
3 0
3 years ago
Other questions:
  • H=4pn<br> How do I solve
    12·1 answer
  • Please help me will give brainliest
    12·1 answer
  • How do you round off 639,121 to the nearest ten thousand?
    12·2 answers
  • I need help! and someone to tell me how to do it<br> step by step i have my exams tmr!
    10·2 answers
  • Please help me ASAP ksjsbdbdjdk
    7·1 answer
  • (BRAINLIEST TO THE PERSON WHO HELPS ME WITH THESE THREE QUESTIONS)
    6·1 answer
  • a shopkeeper bought two radios for Rs 6000.He sold one of them at a profit of 20% and the other at a loss of 10%.If he gained 2%
    15·1 answer
  • What is the value of the 3rd iterate if x0 = 2.4 Carry out your answers to the 5th decimal place
    11·2 answers
  • Find the value of x. Assume that lines which appear to be tangent to the circle are tangent.
    10·1 answer
  • Solve the system of equations using substitution.<br> y = -2X +1<br> 4x + 2y = -2
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!