Question

If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

Answer 1

Question #71632, Math / Statistics and Probability

If $x$ is a normal variable with the mean $u=5$ and variance (sigma square)=16, what is the probability that $x$ is less than or equal to 6?

Answer.

$$P(X < 6) = P\left(Z < \frac{X - \mu}{\sigma}\right) = P\left(Z < \frac{6 - 5}{\sqrt{16}}\right) = P(Z < 0.25) = 0.5987.$$

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