# Thread: Normal Distribution

1. ## Normal Distribution

The wording confuses me. How can this question be done?

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Q: The time taken by a bus to travel between Town A and Town B can be modeled by a normal distribution with Mean $\displaystyle 180$ minutes and Standard Deviation $\displaystyle 12 minutes$. A passenger on the bus needs to be in Town B $\displaystyle t$ minutes after the bus leaves Town A. Find the value of $\displaystyle t$ such that there is only a $\displaystyle 1 \%$ chance the passenger does not arrive in time.

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I understand standardizing should be done but not aware how it should be done? The answer is $\displaystyle 207.9$.

2. Hello air

I assume your taking the S1 exam this month.

let the variable of time taken be T

you want $\displaystyle P(T < t ) = 0.99$

transform the variable to Z

giving $\displaystyle P(Z < \frac{t - 180}{12} ) = 0.99$

now you need to look in your normal distribution table the value of z which gives 0.99. the table I have only has $\displaystyle \Phi (2.32) = 0.9898$ and $\displaystyle \Phi (2.34) = 0.9904$. If your are taking S1 your not expected to interpolate so I'll just take 2.32

giving $\displaystyle \frac{t - 180}{12} = 2.32$

giving $\displaystyle t = 207.84$