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
Tresset [83]
3 years ago
7

The lengths of nails produced in a factory are normally distributed with a mean of 5.02 centimeters and a standard deviation of

0.05 centimeters. Find the two lengths that separate the top 6% and the bottom 6%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Mathematics
1 answer:
zaharov [31]3 years ago
7 0

Answer:

The length that separates the top 6% is 5.1 centimeters.

The length that separates the bottom 6% is 4.94 centimeters.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 5.02, \sigma = 0.05

Find the two lengths that separate the top 6% and the bottom 6%.

Top 6%:

The 100-6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555.

Z = \frac{X - \mu}{\sigma}

1.555 = \frac{X - 5.02}{0.05}

X - 5.02 = 1.555*0.05

X = 5.1

So the length that separates the top 6% is 5.1 centimeters.

Bottom 6%:

The 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.

Z = \frac{X - \mu}{\sigma}

-1.555 = \frac{X - 5.02}{0.05}

X - 5.02 = -1.555*0.05

X = 4.94

The length that separates the bottom 6% is 4.94 centimeters.

You might be interested in
Pease I need help..
Savatey [412]

You would divide 69 (her height) by 12 to get feet, and to get her weight in pounds, you need to multiply her weight in KG by approximately 2.205. Her weight in pounds is 154.324 pounds.

4 0
3 years ago
Factor completely, then place the answer in the proper location on the grid. Write the answer in descending powers of a.
Tatiana [17]
4a⁴ + 6a³b² + 2a²b³ <span>=> 2a²(2a² + 3ab² + b³) </span>
3 0
3 years ago
Read 2 more answers
The cost of having a package delivered has a base fee of $10.80. Every pound over 5 lbs cost an additional $0.41 per pound. Writ
AlladinOne [14]
C=10.8+(x-5)*0.41

Where x is the total weight of the package.
6 0
3 years ago
Read 2 more answers
Choose the correct option that explains what steps were followed to obtain the system of equations below
Dominik [7]

Answer:

option C is the correct answer

Step-by-step explanation:

System A:                                                  System B:

-x - 2y = 7    ........(1)                               -x - 2y = 7    .......(3)  

5x - 6y = -3  ........(2)                                  -16y= 32  ........(4)

Solution for system A: ( -3, -2)

For option A

Multiply the first equation by 3

3(- x - 2y) = 3(7)         ⇒     - 3x - 6y = 21 ........... (5)

Add equation 2 and 5

  5x - 6y = -3

<u> - 3x - 6y = 21</u>

  2x -12y = 18   ⇒  2( x - 6y ) = 2( 9 )    ⇒   x - 6y = 9

Option A is not equal to equation in system B so now we check option B.

 For option B

Multiply the first equation by -5

-5(- x - 2y) = -5(7)         ⇒    5x + 10y = -35 ........... (6)

Add equation 2 and 6

  5x - 6y = -3

<u>   5x + 10y = -35</u>

  10x + 4y = -38   ⇒   2( 5x + 2y ) = 2(-19)    ⇒  5x + 2y = -19

Option B is not equal to equation in system B so now we check option C.

For option C

Multiply the first equation by 5            

5(- x - 2y) = 5(7)         ⇒   - 5x - 10y = 35 ........... (7)

Add equation 2 and 7

  5x - 6y = -3

<u> - 5x - 10y = 35</u>

    0 - 16y = 32   ⇒   -16y = 32

Option C is equal to equation in system b so now we check if the solution to system B is same as system A.  

Solution to system B:

First, we find value of y from equation 4:

-16y = 32   ⇒    y = \frac{32}{-16}   ⇒    y = -2

Now, we put value of y in equation 3 to find value of x:

-x - 2y = 7  ⇒  -x - 2(-2) = 7   ⇒  -x + 4 = 7   ⇒  -x = 7 - 4  ⇒  -x = 3

multiply both sides by -1

-1 × (-x) = -1 × (3)       ⇒     x = -3

Solution of system B = (-3, -2)

Solution of system B is the same as system A, so option C is correct.

6 0
3 years ago
Read 2 more answers
Please help quickly !!!!!!!
telo118 [61]

Answer:

the first one

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • What is 22 percent of 400?
    6·2 answers
  • PLEASE HELP! MATHS QUESTION
    15·1 answer
  • A scatter plot is shown. Data points are located at 1 and 9, 3 and 5, 5 and 6, 4 and 4, 2 and 7, and 6 and 4. A line of best fit
    5·2 answers
  • Sales tax rate is 7.375% in New York State, then how much sales tax would you pay in Albany for a $34 pair of pants
    11·1 answer
  • Find the sum of the first 2,000 positive integers (the numbers 1 through 2000).
    5·1 answer
  • Which algebraic expression is represented by the model?
    14·1 answer
  • Triangle END is reflected across the line y = x using the rule (x, y) → (y, x) to create triangle E′N′D′. If a line segment is d
    15·1 answer
  • The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x= blank
    14·1 answer
  • Write the equation for each line. (will give brainlest)
    8·2 answers
  • Help meh for brainlist
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!