All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

X \sim \mathrm{N}(\mu, \sigma^2)

\mathrm{P}(X \textless 40.0) = 0.05

\Rightarrow \frac{40 - \mu}{\sigma} = -1.6449 \rightarrow (1)

\mathrm{P}(X \textless 70.0) = 0.05

\Rightarrow \frac{70 - \mu}{\sigma} = 1.9600 \rightarrow (1)

Solving, \mu = 53.7 and \sigma = 8.32

KS Comments:

A very straightforward question here, as it didn’t even try to trick unsuspecting students who often forget to change the signs before applying inverse norm function. Please use a Graphing Calculator to solve if you aren’t good with simultaneous equations.

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