Question

a local charity holds a carnival to raise money. in one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. the participant wins the dollar amount marked on the space on which the wheel stops. let x represent the value of a spin. the distribution of x is given in the table.

what is the median of the distribution?

1
1.5
2
2.1

Explanation:

Step1: Calculate cumulative probabilities

The cumulative probability for \(X = 0\) is \(P(X\leq0)=0.4\).
The cumulative probability for \(X = 1\) is \(P(X\leq1)=0.4 + 0.2=0.6\).

Step2: Determine the median

The median \(m\) is the value such that \(P(X\leq m)\geq0.5\) and \(P(X\geq m)\geq0.5\).
Since \(P(X\leq1) = 0.6\geq0.5\) and \(P(X\geq1)=1 - P(X = 0)=1 - 0.4 = 0.6\geq0.5\)

Answer:

1