Let's divide the shaded region into two areas:
area 1: x = 0 ---> x = 2
ares 2: x = 2 ---> x = 4
In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.
Area 1:
Area 2:
Therefore, the area of the shaded portion of the graph is
A = A1 + A2 = 5.34
Answer: 0.0228
Step-by-step explanation:
Given : The mean and the standard deviation of finish times (in minutes) for this event are respectively as :-
If the distribution of finish times is approximately bell-shaped and symmetric, then it must be normally distributed.
Let X be the random variable that represents the finish times for this event.
z score :
Now, the probability of runners who finish in under 19 minutes by using standard normal distribution table :-
Hence, the approximate proportion of runners who finish in under 19 minutes = 0.0228