A machine fills bottles with water. The volume of water delivered by the machine to a bottle is X ml where X N(q, o^2) (mu =q & theta = o)?

[匿名]

2017-05-28 6:06 pm

One of these bottles of water is selected at random.
Given that q = 503 and o = 1.6

1- Find w such that P(1006 – w < X < w) = 0.9426

Following adjustments to the machine, the volume of water delivered by the machine to a
bottle is such that q = 503 and o= T
Given that P(X < r) = 0.01
and P(X > r + 6) = 0.05

2- find the value of r and the value of T

How would I do these? please explain each step that you take , thank you

更新1:

I've worked out how to do question 2 so you don't have to answer that one now

回答 (1)

Lopez

2017-05-29 3:14 pm

✔ 最佳答案

P( 1006 - w < x < w ) = 0.9426
P( ( 1006 - w - q )/o < z < ( w - q )/o ) = 0.9426 , where z ~ N( 0 , 1 )
P( ( 1006 - w - 503 )/1.6 < z < ( w - 503 )/1.6 ) = 0.9426
P( ( 503 - w )/1.6 < z < ( w - 503 )/1.6 ) = 0.9426

Let u = ( w - 503 )/1.6 , we get
P( - u < z < u ) = 0.9426
1 - 2*P( z < - u ) = 0.9426
P( z < - u ) = ( 1 - 0.9426 )/2 = 0.0287

By the table of N( 0 , 1 ) , we have u = 1.9
u = ( w - 503 )/1.6 = 1.9
w = 503 + 1.6*1.9 = 506.04 ..... Ans

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