# question about normal distribution

I'm not being able to identify the mathematical pattern used answer this question:

Suppose that the length of a speficic kind of snake may be modelled by a normal distribution with mean 50.8 (cm) and standard deviation 0.8.

Calculate the length (cm) that is exceeded by only 7% of this specific kind of snake.

What I though:

• Plot the C.D.F and find the 93th percentile (maybe using z-score)?. is that correct?
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## 1 Answer

You're almost there. Find the $\text{z-score}$ of where the CDF is 0.93. In this case, the value is $1.48$. Knowing the Z-score to be $1.48$, perform standardization.

You will get, letting $X$ to be the length of a randomly chosen snake, we attempt to find $$P(X>x) = 0.7$$ Which turns out $$1.48 = \frac {x - \mu}{\sigma}$$

so $$x = 1.48(0.8) + {50.8} = 51.98\text {cm}$$
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