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]
2 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]2 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
Need help ASAP <br> Integrated math ll
Solnce55 [7]

Answer:

∠ EFH = 112°

Step-by-step explanation:

∠ ACD and ∠ EFH are Alternate exterior angles and are congruent, thus

11x - 20 = 9x + 4 ( subtract 9x from both sides )

2x - 20 = 4 ( add 20 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Thus

∠ EFH = 11x - 20 = 11(12) - 20 = 132 - 20 = 112°

7 0
3 years ago
If the ratio of the length of a rectangle to its width is 9/4 and its length is 18 cm, what is the width of the rectangle?
Kruka [31]

Answer:

The width is 8

Step-by-step explanation:

if the ratio of length to width is 9 to 4. and we know the length is 18, 18 is 2 times as much as 9, so 4*2=8.                   9*2=18,4*2=8

6 0
2 years ago
Read 2 more answers
Which shows all the like terms in the expression?
GenaCL600 [577]
4x-3+7x+1

Ones with a variable: 4 & 7
Only whole number: -3 & 1

The answer is option two: -3 and 1; 4x and 7x
7 0
3 years ago
Read 2 more answers
What was the impact of the olive branch petition
gizmo_the_mogwai [7]
It failed to bring about peace and only angered King George III

The Olive Branch petition was a final attempt by the colonists to avoid going to war with Britain. The purpose was to appease King George III and prevent the conflict between the colonies and Britain from escalating into a full blown war. However, the king refused to read it. And then came the war.
5 0
3 years ago
If D is the midpoint of the segment AC and C is the midpoint of segment DB , what is the length of the segment AB , if AC = 3 cm
Juliette [100K]
<span>A midpoint divides a line or a segment into two equal parts. If D is the midpoint of the segment AC and C is the midpoint of segment DB, what is the length of the segment AB, if AC = 3 cm.</span>

 

If D is the midpoint of AC, then AD=DC

If C is the midpoint of DB, then DC=CB

If AC=3cm. then then DC-3/2=1.5

If DC=1.5 then CB is 1.5 also

AB=AC+CB

AB=3+1.5

AB=4.5

5 0
3 years ago
Other questions:
  • Solve the inequality for x, assuming that a, b, and c are positive constants.
    10·1 answer
  • I need some help with this problems.I will apreciate the answers:)))))
    6·1 answer
  • Eight times a number plus five times another number is -13. The sum of the number is 1. What are the nymber?
    6·1 answer
  • the probability of pulling a red marble out of bag of colored marbles is 3:7.if you were to pull color marbles out of the bag (o
    11·1 answer
  • Help!!! How do I do problems like these
    13·1 answer
  • Use the figure below and determine the value of x<br> PLS HELP
    5·2 answers
  • 50 POINTS: Please help thank you so much!! (Image attached) The polygons are similar. Find the values of the variables.
    14·1 answer
  • Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is 882, and t
    14·1 answer
  • 85% of fans going to a baseball game will spend at least $7.00 on food at the ballpark.
    11·1 answer
  • Estimate √700 to one decimal place.​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!