Continuous distributions

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

Waiting for the bus

timeline from one to two pm with six bus arrivals, one every 12 minutes.png

Set of axes with wait time on the x axis.png

Y axis of P(outcome = wait time) with a horizontal line going across the graph at 1/12.png

$$P(4 \le \text{wait time} \le 7) = ~~ ?$$

Area between four and seven highlighted under the horizontal line.png

$$P(4 \le \text{wait time} \le 7) = ~~ ?$$

Width of highlighted area is seven minus four equals three, height is one twelfth.png

$$P(4 \le \text{wait time} \le 7) = 3 \times 1/12 = 3/12$$

Width of highlighted area is seven minus four equals three, height is one twelfth.png

$$ P(\text{wait time} \le 7) = ~~ ?$$

$$ P(\text{wait time} \le 7) = \frac{7-0}{12} $$

$$ P(\text{wait time} \le 7) = \frac{7}{12} = 58.33\% $$

Area highlighted from zero to seven under horizontal line.png

$$P(0 \le \text{wait time} \le 12) = ~~ ?$$

Width of distribution equals one, height equals one twelfth.png

$$P(0 \le \text{outcome} \le 12) = 12 \times 1/12 = 1$$

Width of distribution equals one, height equals one twelfth.png

$$ P(\text{wait time} \ge 7) = 1 - \frac{7}{12} $$

$$ P(\text{wait time} \ge 7) = \frac{5}{12} = 41.67\% $$

Area highlighted from seven to 12.png

Distribution with two peaks.png

Introduction to Statistics