Gaussian PDF: Probability of P(x), Usable Shafts %

[axnman]

Que. 1 Consider a Gaussian PDF with µ = 20, σ = 30, a = 50 and b =80. Determine i)Probability that P(x>b)
ii)P(x ≤ b)
iii)P(x ≤ - b)
iv)P(a ≤ x ≤ b)


Que. 2 In a certain manufacturing process only shafts whose diameters are less than 1.5 inches can be used. Given the shaft diameters are normally distributed with mean (µ) 1.490 inches and standard deviation (σ) 0.005 inches, determine the percentage of shafts that are usable.
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[scottie_000]

We can't just give you the answers...you need to show some working
Do you know how to turn a normal distribution into a standard normal distribution?
That is always the key to determining probabilities

You have all the information you'll need once you scale "a" and "b" correctly using the mean and standard deviation given

If you don't know how to manipulate the figures then i'll give you some hints

 

[axnman]

z = (X - µ ) / σ...am talking @ que. 2...This way z = (1.5-1.49) / 0.005 = 2...Then i get confused as i have to look into the tables...I get 0.0228...hmmm so well the answer should be 100 - 0.0228 % of shafts = 97.72%...Is that correct?

Q 1 am still trying...

 

[scottie_000]

Your answer to q2 looks pretty reasonable

For q1, follow the same lines as you did for q2
i.e. find z, then look up phi(z) in tables. Draw a bell curve if you have to etc.