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
tensa zangetsu [6.8K]
3 years ago
8

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch. Suppose that the speci

fications require the dot diameter to be between 0.0014 and 0.0026 inch. If the probability that a dot meets specifications is to be 0.9963, what standard deviation is needed? Round your answer to 4 decimal places.
Mathematics
1 answer:
Leni [432]3 years ago
7 0

Answer:

0.0002 inch

Step-by-step explanation:

The empirical rule of the normal distribution, the 68-95-99.7 rule, means

if the mean is <em>μ</em> and the standard deviation is <em>σ</em>,

68% of data lies within <em>μ </em>- <em>σ</em> and <em>μ </em>+ <em>σ</em>,

95% of data lies within <em>μ </em>- 2<em>σ</em> and <em>μ </em>+ 2<em>σ</em>,

99.7% of data lies within <em>μ </em>- 3<em>σ</em> and <em>μ </em>+ 3<em>σ.</em>

<em />

From the question, <em>μ</em> = 0.002.

The required range is 0.0014 to 0.0026.

With a probability of 0.9963, then 0.9963 × 100% = 99.63% should lie within the range. This approximately corresponds to <em>μ </em>- 3<em>σ</em> and <em>μ </em>+ 3<em>σ.</em>

<em>μ </em>- 3<em>σ</em> = 0.0014

0.002 - 3<em>σ</em> = 0.0014

3<em>σ</em> = 0.0006

<em>σ</em> = 0.0002

Hence, the standard deviation is 0.0002 inch

We can check with the other end of the range:

<em>μ </em>+ 3<em>σ</em> = 0.0026

3<em>σ</em> = 0.0026 - 0.002

3<em>σ</em> = 0.0006

<em>σ</em> = 0.0002

You might be interested in
Simplify the expression using trigonometric identities: sec (–θ) – cos θ.
ololo11 [35]

Answer:

sin θ . tan θ

Step-by-step explanation:

Note : -

sec ( - θ ) = sec θ

Formula / Identity : -

sec θ = 1 / cos θ

sec ( - θ ) - cos θ

= [ 1 / cos θ ] - cos θ

{ LCM = cos θ }

= [ 1 / cos θ ] - [ cos²θ / cos θ ]

= [ 1 - cos²θ ] / cos θ

{ 1 - cos²θ = sin²θ }

= sin²θ / cos θ

{ sin²θ = sin θ . sin θ }

= sin θ . sin θ / cos θ

{ sin θ / cos θ = tan θ }

= sin θ . tan θ

Hence, simplified.

4 0
2 years ago
Find the solution to the following system of linear
mrs_skeptik [129]

Step-by-step explanation:

y = 4x - 4 \\ x + y = 11 \\ x + 4x - 4 = 11 \\ 5x = 15 \\ x = 3 \\ y = 4 \times 3 - 4 \\ y = 8

8 0
2 years ago
(7x – 10) – (–6x – 8).
xeze [42]

Answer:

13x-2

Step-by-step explanation:

1) distribute the negative sign to each term in the second parentheses

(7x-10)-(-6x-8)

7x-10+6x+8

2) combine like terms

7x+6x= 13x

-10+8=-2

13x-2

Hope this helps!

4 0
2 years ago
What is the yintercept of f(x) = (3/5)^x<br> A: (1,3/5)<br> B: (1,0)<br> C:(0,0)<br> D: (0,1)
zysi [14]

Answer:

I think its A

Step-by-step explanation:

5 0
3 years ago
Samantha is making flower arrangements. She has 32 roses and 96 daisies. If she wants to make all the arrangements identical and
-Dominant- [34]

Answer:

3 daisies.

Step-by-step explanation:

Given that,

Samantha has 32 roses and 96 daisies.

She wants to make all the arrangements identical and have no flowers left over. We need to find the no of daisies in each flower arrangement.

For this, we need to first find the HCF of 32 and 96.

The factors of 32 are: 1, 2, 4, 8, 16, 32

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

HCF = 32

No of daisies = 96/32 = 3

Hence, there are 3 daisies in each flower arrangement.

7 0
3 years ago
Other questions:
  • The Symphony
    5·1 answer
  • I need help with my math work online can anyone help???
    7·1 answer
  • What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem?
    7·1 answer
  • 15. Thirty divided by seven times a number
    5·2 answers
  • Twice a number decreased by four is greater than ten, what numbers satisfy this condition?
    7·2 answers
  • No offence but can everybody quit going ASAP or HURRY its annoying btw free points
    5·1 answer
  • Daniel watches one hour of television for every three hours of homework he does each week. If you did 15 hours of homework last
    7·2 answers
  • What is the equation of the line that passes through the points (-4,-1) and (6,-1)
    7·1 answer
  • What’s the equation.
    13·1 answer
  • For Thanksgiving Break Nykouth and her family is going to visit relatives in Nebraska. Her dad has found a hotel room at the Hil
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!