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CaHeK987 [17]
3 years ago
14

A package delivery service divides their packages into weight classes. suppose that packages in the 14 to 20 pound class are uni

formly distributed, meaning that all weights within that class are equally likely to occur. find the 40th percentile of packages weights in this weight class.
Mathematics
1 answer:
nexus9112 [7]3 years ago
6 0

Answer: yy - \alpha \alpha = Percentile (\beta \beta -\alpha \alpha )

yy = 0.40 (20 - 14) + 14[tex] yy = 2.4 + 14

yy = 16.4

Thus, 16.4 pound class belongs to the 40th percentile of the weight class.

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Answer:Given:

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By the law of complements,

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By the law of total probability,

P(B)=P(B|A)*P(A)+P(B|A)*P(~A)

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Note: get used to working in fraction when doing probability.

(a) Find P(A|B):

By Baye's Theorem,

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(b) Find P(~A|~B)

We know that

P(~A)=1-P(A)=399/400

P(~B)=1-P(B)=133/136

P(A∩B)

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=9/4000

P(A∪B)

=P(A)+P(B)-P(A∩B)

=1/400+51/500-9/4000

=409/4000

P(~A|~B)

=P(~A∩~B)/P(~B)

=P(~A∪B)/P(~B)

=(1-P(A∪B)/(1-P(B)) [ law of complements ]

=(3591/4000) ÷ (449/500)

=3591/3592

The results can be easily verified using a contingency table for a random sample of 4000 persons (assuming outcomes correspond exactly to probability):

===....B...~B...TOT

..A . 9 . . 1 . . 10

.~A .399 .3591 . 3990

Tot .408 .3592 . 4000

So P(A|B)=9/408=3/136

P(~A|~B)=3591/3592

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