Normal Distribution - Calculations (Edexcel A-Level Mathematics): Flashcards

$X$ is normally distributed, mean 30, SD 3 ($\sqrt{9}$).

Calculate area right of $30$ using Normal CD function.

$P(X \geq k)$ equals $P(X > k)$ due to thin strips having area 0.

$P(X \geq \text{mean}) = 0.5$ for normal distributions.

The curve is bell-shaped and symmetrical around the mean.

Use a very large number like $1E10$ for infinity.

Use Normal CD with Lower: -999999, Upper: 18, SD.

$P = 0.0766$, indicating $7.66\%$ of women are shorter.

$P = 0.1906$ for women in that height range.

$P(X \geq 5) = 1 - P(X \leq 4)$ using binomial distribution.