Question

hannah has a chicken coop with 6 hens. let x represent the total number of eggs the hens lay on a randomly chosen day. the distribution for x is given in the table. what is the median of the distribution? 3 3.5 4 4.2

Explanation:

Step1: Calculate cumulative probabilities

Cumulative probability for \(0\) eggs: \(P(X = 0)=0.02\)
Cumulative probability for \(1\) eggs: \(P(X\leq1)=0.02 + 0.03=0.05\)
Cumulative probability for \(2\) eggs: \(P(X\leq2)=0.05+ 0.07 = 0.12\)
Cumulative probability for \(3\) eggs: \(P(X\leq3)=0.12+0.12 = 0.24\)
Cumulative probability for \(4\) eggs: \(P(X\leq4)=0.24 + 0.30=0.54\)

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 \(P(X\leq4) = 0.54\geq0.5\) and \(P(X\geq4)=1 - P(X\leq3)=1 - 0.24 = 0.76\geq0.5\)

Answer:

\(4\)