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? Show work please!

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

expected value of points awarded for a race is 2.25

Step-by-step 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