Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

Sagot :

fichoh

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

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.