- #1
LDC1972
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Homework Statement
Metal strips are produced mean length 150cm, standard deviation 10cm.
Find probability that length of random strip is:
a/ shorter than 165cm
b/ longer than 170cm
c/ between 145 and 155cm
Homework Equations
Z = x - μ / σ
θ (Z) - θ (z) = average probability (question c)
The Attempt at a Solution
a/ Z = 165 - 150 / 10 = 1.5
1.5 from standardised table = 0.9332 = 93.32% probability length shorter than 165cm
b/ Z = 170 - 150 / 10 = 2
2 from standardised table = 0.9772
Now here I did 1 - 0.9772 = 0.0228 = 2.28% probability length longer than 170cm.
I did this not because I understand the curve graph, but because without subtracting 1 the probability was obviously wrong.
c/ as per a/ to get Z = -0.5 for 145cm and Z = 0.5 for 155cm
used tables to get 0.6915 for 0.5.
Then did:
θ = 0.6915 - (1 - 0.6915) = 0.383 = 38.3% between 145 and 155 cm
Again, I had to -1 to make equation work anyway, BUT also to give a sensible probability.
I'm assuming answers are right? But how do we say when to -1 or not. I know it' to left or right of mean etc, but simply can't get head round it?
Any help welcome as always!
Thanks guys.
Oh I know θ should be O with vertical line, but couldn't find it on the selection box, so made do..