Complete question :
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. Her coach used her statistics from last season to design a simulation using a random number generator to predict how many points she would receive in her first race this season.
What is Sandra’s expected value of points awarded for a race?
Integer Value Points Awarded Frequency
1-8 3 20
9-15 2 12
16-19 1 6
20 0 2
Answer:
expected value of points awarded for a race is 2.25
Explanation:
Data given:
Integer Value - - Points Awarded - - Frequency
1-8 - - - - - - - - - - - - - 3 - - - - - - - - - - - - - - 20
9-15 - - - - - - - - - - - - 2 - - - - - - - - - - - - - - 12
16-19 - - - - - - - - - - - - 1 - - - - - - - - - - - - - - -6
20 - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - 2
Expected value(E) :
Score * probability of score
That is;
E = x * p(x)
From the data generated:
Probability of each score :
Probability = required outcome / Total possible outcomes
Total possible outcomes = (20+12+6+2) = 40
P(score(x) = 3) = 20/40 = 0.5
P(score(x) = 2) = 12/40 = 0.3
P(score(x) = 1) = 6/40 = 0.15
P(score(x) = 0) = 2/40 = 0.05
Expected score :
[(3*0.5) + (2*0.3) + (1*0.15) + (0*0.05)]
[1.5 + 0.6 + 0.15 + 0]
= 2.25