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S1 tricky Q help!

I'm having trouble with this question-appreciate any help!

A courier company sends parcels by van between its 2 depots. Found that 10% of journeys take less than 3 hours and 20% take more than 3.5 hours. you may assume the times are normally distributed. Calculate the mean and standard deviation of the times.
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Avatar for BCHL85
BCHL85
12
Let X be the time needed
Then X ~ N(m, v)
So change to Z = (X - m)/rt(v)
Z ~ N(0, 1)
So you'll get
P(X < 3) = P(Z < (3-m)/rt(v)) = 10%
and
P(X > 3.5) = P(Z > (3.5-m)/rt(v)) = 20%
-> P(Z < (3.5-m)/rt(v)) = 80%

Compare with the table to find out values of
(3 - m)/rt(v) and (3.5-m)/rt(v)
Solve 2 equations to find m and v

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