Question

Let X be a random variable having normal distribution with mean 48 and standard deviation 10.Then find (X≤41).

Answer 1

Question #12774

Let $X$ be a random variable having normal distribution with mean 48 and standard deviation 10. Then find $P(X \leq 41)$.

Solution.

Denote by $Y$ a random variable that has standard normal distribution $Y \sim N(0,1)$. One has $P(X \leq 41) = P\left(\frac{X - 48}{10} \leq \frac{41 - 48}{10}\right) \approx P(Y \leq -0.7) = \Phi(-0.7)$, where $\Phi()$ stands here for the distribution function of standard normal distribution. The last approximately equals 0.24.

Answer. 0.24.