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pychu [463]
4 years ago
8

PVC pipe is manufactured with mean diameter of 1.01 inch and a standard deviation of 0.003 inch. Find the probability that a ran

dom sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.
Mathematics
1 answer:
oksian1 [2.3K]4 years ago
6 0

Answer: 0.8186

Step-by-step explanation:

Given: Mean : \mu=1.01\text{ inch}

Standard deviation :  \sigma=0.003\text{ inch}

Sample size :  n=9

The formula to calculate z-score :-

z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For x=1.009 inch

z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1

For x=1.012 inch

z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2

Now, The p-value =P(-1

Hence, the required probability = 0.8186

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The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

<h3>What are Trigonometric functions?</h3>

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\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\

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1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

Learn more about Trigonometric functions:

brainly.com/question/6904750

#SPJ1

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