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
Ksenya-84 [330]
10 months ago
15

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviat

ion of 0.07 millimeters. Find the two diameters that separate the top 3% and the bottom 3%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Mathematics
1 answer:
dimulka [17.4K]10 months ago
7 0

As per the concept of normal distribution, the two diameters of the bolt that has separate the top 3% and the bottom 3% are 5.2836 mm and 5.0764 mm respectively .

Normal distribution:

Normal distribution means the probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean and it has the bell shaped curve.

Given,

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviation of 0.07 millimeters.

Here we need to find the two diameters that separate the top 3% and the bottom 3% and these diameters could serve as limits used to identify which bolts should be rejected. we have also round off the result into nearest hundredth.

Here we have the given question with the values of,

The value of Mean is 5.18 millimeters

The value of Standard deviation is 0.07 millimeters.

Here we have to consider the following two cases, they are.

Case 1

We need to find x₁ such that that is P(X > x₁) = 3% when we convert it into decimal then we get P (X > x₁) = 0.03

So, as per the probability,

P (X ≤ x₁) = 1 - 0.03 = 0.97

So, z corresponding to the value of p = 0.97 is 1.48

Apply the given values to the formula of normal distribution then we get,

=> 1.48 = (x₁ -  5.18) /0.07

=> 0.1036 = x₁ - 5.18

Therefore, the value of x₁ is  5.2836

So, the diameter of the both with separate top 3% is 5.2836.

Case 2:

Next we have to take P(X < x₂) = 3% when we convert it into decimal then we get P (X < x₂) = 0.03

So, as per the given probability, the value of

P (X ≤ x₂) = 1 - 0.03 = 0.97

So, z corresponding to but here we have to use the negative because of the less than concept p = 0.97 is -1.48

Apply the values on the formula of normal distribution then we get,

-1.48 = (x₂ -  5.18) /0.07

Move the value to the other side

-0.1036 = x₂ - 5.18

When we simplify it,

x₂ =  5.0764

So, the diameter of the both with separate bottom 3% is 5.0764

To know more about Normal distribution here.

brainly.com/question/12421652

#SPJ1

You might be interested in
What does first difference mean?
Sunny_sXe [5.5K]

Answer:

In statistics and econometrics, the first-difference (FD) estimator is an estimator used to address the problem of omitted variables with panel data. It is consistent under the assumptions of the fixed effects model. In certain situations it can be more efficient than the standard fixed effects (or "within") estimator.

First differences are the differences between consecutive y-‐values in tables of values with evenly spaced x-‐values. If the first differences of a relation are constant, the relation is _______________________________ If the first differences of a relation are not constant, the relation is ___________________________

4 0
2 years ago
Read 2 more answers
What to do do I subtract the corridnates or add them
Mandarinka [93]
I think its subtracting 
8 0
3 years ago
Pls help, algebra 1<br>​
AURORKA [14]

Answer:

20, 35, 50

Step-by-step explanation:

8 0
2 years ago
Jose can paint an entire house in seven hours and brandon can paint the same house in eight hours. Write an equation that can be
guajiro [1.7K]

Answer:

t/8 + t/7 = 1

Step-by-step explanation:

Given in the question that,

time require for Jose to paint the house = 7 hours

time require for Brandon to paint the house = 8 hours

Suppose t means Full house painted.

<h3>To solve the question we have to figure out how much each of them can paint in ONE hour.</h3>

7 hours----t

1 hour ---- t/7

8 hours----t

1 hour ---- t/8

<h3>Equation</h3>

t/8 + t/7 = 1 (in one hour)

(7t + 8t)/8(7) = 1

15t/56 = 1

15t = 56

t = 56/15

t = 3.73 hours

5 0
2 years ago
What is the result of subtracting the second equation from the first?
Ronch [10]

Answer:

-5x + 0y = -11

The y terms are eliminated

Step-by-step explanation:

- 4x – 2y = -2

X - 2y = 9

We want to subtract the second equation from the first

Distribute a minus sign to all the terms in the second equation

- 4x – 2y = -2  

X - 2y = 9

= (-5x + 0y = -11)

6 0
3 years ago
Other questions:
  • What is the estimate to 8,244?
    5·1 answer
  • A pastry recipe calls for 3 cups of flour to make 8 servings. how many cups of flour are needed to make 6 servings?
    13·2 answers
  • hello! So the people in Indian server were bad(as they would not answer and instead spam) so I switched servers and I hope you a
    5·1 answer
  • What is the least common multiple of x^2 + 11
    6·1 answer
  • C + G + I +F is the formula to determine GDP. What does the G in the formula represent?
    5·1 answer
  • 3. A rectangular prism has dimensions of 1 , 2, and in. (a) What is the volume of the prism? Show your work and express your ans
    7·1 answer
  • Which expression correctly represents the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide?
    12·1 answer
  • Find the sum or difference of 2/3 + 5/6​
    6·1 answer
  • Four years after a tree was planted, its height was 6 feet. Eight years after it was planted, its height was 8 feet. How tall wi
    12·2 answers
  • Find the value of c that makes the expression a perfect square trinomial. x2 + 9 4 x + c
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!