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ahrayia [7]
3 years ago
15

The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation o

f time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less
Mathematics
1 answer:
faust18 [17]3 years ago
6 0

Answer:

required probability is 0.8413

Step-by-step explanation: Given mean \mu =15 minutes, standard deviation \sigma =4 seconds, we need to find P\left ( X\leq 19 \right ). Using z score

z=\frac{X-\mu }{\sigma }\\=\frac{19-15}{4}\\=1

So,

P\left ( X\leq 19 \right )\\=P\left ( Z\leq 1 \right )\\=0.8413

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The right triangle is assumed to be inscribed in the rectangle, such that

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  • The length of the hypotenuse of the triangle is <u>26 cm</u>.

Reasons:

Let <em>x</em> and<em> </em><em>y</em> represent the length of the sides of the rectangle

Whereby the base and height of the right triangle are the same as the

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Perimeter of the rectangle = 2·x + 2·y = 68

Therefore;

\displaystyle x + y = \frac{68}{2} = 34

x + y = 34

The base of the right triangle = x

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By Pythagoras's theorem, the length of the hypotenuse side = √(x² + y²)

Therefore; Perimeter of the right triangle = x + y + √(x² + y²) = 60

Which gives;

∴√(x² + y²) = 60 - (x + y) = 60 - 34 = 26

The length of the hypotenuse side, √(x² + y²) = <u>26 cm</u>

Learn more about Pythagoras's theorem here:

brainly.com/question/8171420

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