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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

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fomenos

Answer:

4 bags of chocolate chips and 1 bag of walnuts.

Step-by-step explanation:

Find how many ounces are in 3 pounds:

16 oz = 1 lb

16 oz × 3 = 3 lbs

48 oz = 3 lbs

Variable x = number of chocolate chips

Variable y = number of walnuts

4x + 1y = 15

Keep in mind it must equal up to 48 oz and be $15 or under.

4 bags × 12 oz = 48 oz

1 bag × 4 oz = 4 oz

48 oz + 4 oz = 52 oz > 48 oz

4 bags × $3 = $12

1 bag × $2 = $2

$12 + $2 = $14 < $15

Both requirements have been met.

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2 years ago
Find the radius r of C.
garik1379 [7]

Answer:

10

Step-by-step explanation:

By Pythagoras' Theorem:

16 + r = √(24^2 + r^2)

(16 + r)^2 = 24^2 + r^2

256 + 32r + r^2 = 576 + r^2

32r = 320

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5 0
3 years ago
Given: △CGF ,CG=GF=CF=and, KOPS is a square inside this triangle with one side on CF and its two vertices on CG and GF
shepuryov [24]

Answer:

  AKPOS/ACGF = 28√3 -48 ≈ 0.497423

Step-by-step explanation:

Let's assume the square is a unit square. Then the height of the triangle is ...

  1 +(√3)/2 = h

and half the base of the triangle is ...

  h/√3 = (√3)/3 +1/2 = b/2

The area of the triangle is the product of these:

  A = (1/2)bh

  = (2 +√3)/2 × (3 +2√3)/6

  = (6 +3√3 +4√3 +6)/12 = (12 +7√3)/12

So, the ratio of the area of the square to that of the triangle is the inverse of this, or ...

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3 years ago
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Step-by-step explanation:

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3 years ago
Help needed math 3 - 10 points read closely
inessss [21]
<h2>Hello!</h2>

The answer is:

The answer is the fourth option,

f(-3)=-\frac{1}{3}

<h2>Why?</h2>

Piecewise functions are functions that are composed by two or more expressions, the expression to use will depend of the domain or input that we need to evaluate.

We are given the piecewise function:

\left \{ {{\frac{1}{x}, if x

There, we know that:

We should use the first expression if the value to evaluate is less than -2.

So, for this case, the function will be:

f(x)=\frac{1}{x}

We should use the second expression if the value to evaluate is greater or equal than 2.

So, for this case, the function will be:

f(x)=x^{2}

Now, since we are given that the value to evaluate is -3, and its less than -2, we need to use the first expression, and evaluate it.

-3

So, evaluating the function we have:

f(x)=\frac{1}{x}

f(-3)=\frac{1}{-3}

f(-3)=-\frac{1}{3}

Hence, we have that the answer is the fourth option,

f(-3)=-\frac{1}{3}

Have a nice day!

7 0
3 years ago
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