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
kirza4 [7]
3 years ago
5

Production of a gas flow meter takes place in two distinct operations. Measurements (n = 15) of the time required for the first

operation yield sample mean and standard deviation of 45 min and 4 min, respectively. Measurements (n = 15) of the time required for the second operation yield sample mean and standard deviation of 32 min and 2.5 min, respectively. For the purposes of this question, assume each time is a normally‐distributed random variable. a) What is the probability that the time required to complete both of those steps will exceed 80 min? b) What is a 95% confidence interval for the expected total time required to produce one flow meter? c) What is a 95%
Mathematics
1 answer:
Karolina [17]3 years ago
4 0

Answer:

a) P(a > 80) = 0.323

b) The 95% confidence interval = (73.40, 80.60)

c) The 95% confidence interval expresses that the mean of the distribution can always be found in the given range, with a 95% confidence level.

Step-by-step explanation:

X ~ (45, 4)

Y ~ (32, 2.5)

(X+Y) ~ (77, 6.5)

Let a = (X+Y)

a) Probability that the time required to complete both of those steps will exceed 80 min = P(a > 80)

This is a normal distribution problem

We then standardize 80 min time

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (a - μ)/σ = (80 - 77)/6.5 = 0.46

To determine the probability the time required to complete both of those steps will exceed 80 min = P(a > 80) = P(z > 0.46)

We'll use data from the normal probability table for these probabilities

P(a > 80) = P(z > 0.46) = 1 - P(z ≤ 0.46) = 1 - 0.677 = 0.323

b) 95% confidence interval for the expected total time required to produce one flow meter.

We need to obtain the margin of error

Margin of error = (critical value) × (standard error of the sample)

Critical value for a 95% confidence interval = critical value for a significance level of 5% = t(15-1, 0.05/2) = 2.145 (using the t-score since information on the population mean and standard deviation isn't known)

Standard error for the sample of sum of times = (standard deviation of the sum of times)/√n = (6.5/√15) = 1.678

Margin of error = 2.145 × 1.678 = 3.60

Limits of the confidence interval = (Sample mean ± margin of error)

Lower limit of the confidence interval = (Sample mean - margin of error) = 77 - 3.60 = 73.40

Upper limit of the confidence interval = 77 + 3.60 = 80.60

The confidence interval = (73.40, 80.60)

You might be interested in
Factories <br>(a+b)^3+8c^3​
Rom4ik [11]

Answer:

(a + b + 2c)(a² + 2ab + b² - 2ac - 2bc + 4c²)

Step-by-step explanation:

Given

(a + b)³ + 8c³ ← this is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

Thus

(a + b)³ + 8c³

= (a + b)³ + (2c)³

= (a + b + 2c)( (a + b)² - 2c(a + b) + (2c)² )

= (a + b + 2c)(a² + 2ab + b² - 2ac - 2bc + 4c²)

8 0
3 years ago
0.9278 round to the nearest tenth
Zarrin [17]
0.9 is 0.9278 rounded to the nearest tenth. Hope this helps!
7 0
3 years ago
Read 2 more answers
What is the simplified form of the following expression? 7(3sqrt2x)-3(3sqrt16x)-3(3sqrt8x)
coldgirl [10]

Assignment: \bold{Simplify \ Equation: \ 7\left(3\sqrt{2}x\right)-3\left(3\sqrt{16}x\right)-3\left(3\sqrt{8}x\right)}

<><><><><><><>

Answer: \boxed{\bold{3\sqrt{2}x-36x}}

<><><><><><><>

Explanation: \downarrow\downarrow\downarrow

<><><><><><><>

[ Step One ] Remove Parenthesis (a) = a

\bold{7\cdot \:3\sqrt{2}x-3\cdot \:3\sqrt{16}x-3\cdot \:3\sqrt{8}x}

[ Step Two ] Simplify Equations

\bold{7\cdot \:3\sqrt{2}x: \ 21\sqrt{2}x}

\bold{3\cdot \:3\sqrt{16}x: \ 36x}

\bold{3\cdot \:3\sqrt{8}x: \ 18\sqrt{2}x}

[ Step Three ] Rewrite Equation

\bold{21\sqrt{2}x-36x-18\sqrt{2}x}

[ Step Four ] Add Similar Elements

\bold{21\sqrt{2}x-18\sqrt{2}x=3\sqrt{2}x}

[ Step Five ] Rewrite Equation

\bold{3\sqrt{2}x-36x}

<><><><><><><>

\bold{\rightarrow Mordancy \leftarrow}

7 0
3 years ago
A 2-inch-wide frame is to be built around theregular decagonal window shown. At what angles a and bshould the corners of each pi
OLEGan [10]
Right angles is one angle.
7 0
3 years ago
Circumference of a circle with radius 10 in
azamat
2*pi*10=62.83 is certainly your answer
5 0
2 years ago
Read 2 more answers
Other questions:
  • Solve. −4.2y+2.1&gt;−2.52 Drag and drop a number or symbol into each box to show the solution. &lt;&gt;0.11.14.62−4.62 y
    9·2 answers
  • Write three DIFFERENT properties that are equivalent to 3 4
    12·1 answer
  • Can SOMONE answer this please
    7·1 answer
  • (3 - (m – p)) = 3; use m = 4, and p = 4<br> Evaluate using the values given
    5·2 answers
  • “Jessica has $300 to buy supplies for her painting. 
    15·2 answers
  • Write the algebraic rule to describe the translation P(-8,6)_P(-10,2)
    13·1 answer
  • Write an equation that represents the graph
    5·1 answer
  • you and 2 friends go out to dinner. The food bill comes to $35.20, and you are charged an aditional 6% sales tax. You then want
    6·2 answers
  • What is -78.6 (-2.4)?<br> A. -188.64<br> B. -32.75<br> C. 32.75<br> D. 188.64
    12·2 answers
  • Which equation gives the sum of...<br> S=0.2/1-8<br> S=1/8-0.2<br> S=8/0.2-1<br> S=8/1-0.2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!