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murzikaleks [220]
3 years ago
14

A data scientist studying a manufacturing process classifies each item produced by the process as either Poor, Acceptable, or Ex

cellent. Assume that the classes of different items are independent of each other and that each item falls into the classes according to the following probabilities:
Poor Acceptable Excellent
0.25 0.6 0.15

The data scientist receives three items produced by the manufacturing process.
Find the chance that:
a. all of items are Acceptable
b. none of the items is Acceptable
c. at least one of the items is Excellent
d. not all of the items are Excellent
e. there is one item of each class
Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0

Answer:

0.214 ; 0.064 ; 0.3859 ; 0.9966 ; 0.135

Step-by-step explanation:

Given the distribution :

Poor ___ Acceptable ____ Excellent

0.25 _____ 0.6 _________ 0.15

The data scientist receives three items produced by the manufacturing process.

Find the chance that:

a. all of items are Acceptable

0.6 * 0.6 * 0.6 = 0.6^3 = 0.214

b. none of the items is Acceptable

P(not acceptable) = 1 - p(acceptable) = 1 - 0.6 = 0.4

0.4 * 0.4 * 0.4 = 0.4^3 = 0.064

c. at least one of the items is Excellent

P(atleast one) = 1 - P(none)

P(not excellent) = 1 - 0.15 = 0.85

P(none is excellent) = 0.85^3 = 0.614125

Hence,

P(atleast one is excellent) = 1 - 0.614125 = 0.3859

d. not all of the items are Excellent

P(not all) = 1 - p(All)

P(all excellent) = 0.15^3 = 0.003375

P(not all are excellent) = 1 - 0.003375 = 0.9966

e. there is one item of each class:

P(poor) * p(acceptable) * p(excellent) * (number of classes)!

0.25 * 0.6 * 0.15 * 3!

= 0.135

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navik [9.2K]

Answer:

<h3>The answer is 10 units</h3>

Step-by-step explanation:

The distance between two points or a line segment can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 1) and (2, 9)

The length of segment AB is

|AB|  =  \sqrt{ ({ - 4 - 2})^{2}  +  ({1 - 9})^{2} }  \\  =  \sqrt{( { - 6})^{2}  +   ({ - 8})^{2} }  \\  =  \sqrt{36 + 64}  \\  =  \sqrt{100}  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 10 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:

We have the final answer as

<h3>10 units</h3>

Hope this helps you

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3 years ago
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Well a difference is the difference between them. difference means subtraction. So so a difference can be written as:
40.67 - (-41.29)

If you subtract a negative number you really add it. to make sense of this you could say 40.67 is 40.67 units away from zero in the positive direction. whereas -41.29 is 41.29 units away in the negative direction. since they go in opposite directions away from zero that means that thw length between them is extended and must then be added together. So
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Answer:

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Step-by-step explanation:

(4+6i)^{2} is essentially (4+6i)(4+6i) (you are squaring (4+6i), so multiplying it by itself), so to simplify, you would need to distribute.

A good way to go about this is using the F.O.I.L. method, multiplying the First numbers in the parentheses, then the Outers, then Inners, and finally, Lasts.

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To write the expression in standard form, though, just order the terms from highest to lowest power!

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