Question

jasmine counted all the beads in each necklace at the jewelry store where she works. x is the number of beads that a randomly chosen necklace had. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Calculate total number of necklaces

Total number of necklaces \(=1 + 3+3+3=10\)

Step2: Calculate sum of \(x\times P(x)\)

For \(x = 95\), \(P(x)=\frac{1}{10}\), \(95\times\frac{1}{10}=9.5\)
For \(x = 116\), \(P(x)=\frac{3}{10}\), \(116\times\frac{3}{10}=34.8\)
For \(x = 127\), \(P(x)=\frac{3}{10}\), \(127\times\frac{3}{10}=38.1\)
For \(x = 191\), \(P(x)=\frac{3}{10}\), \(191\times\frac{3}{10}=57.3\)

Step3: Calculate expected value

\(E(X)=9.5 + 34.8+38.1+57.3=142.4\)

Answer:

142.4