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Question
Math
Posted 3 months ago

Kelsie works at a bicycle shop as a salesperson. She records the number of bicycles she sells on a daily basis. Here is the probability distribution of B=B= the number of bicycles Kelsie sells on a randomly selected day, and T=T= the time she spends filling out daily sales reports.
\begin{tabular}{lcccc}
\hlineB=#B=\# of bicycles sold & 0 & 1 & 2 & 3 \\
T=T= time (minutes) & 0 & 10 & 20 & 30 \\
Probability & 0.30 & 0.50 & 0.15 & 0.05
\end{tabular}

Find the expected value of the amount of time Kelsie spends filling out daily sales reports.
E(T)=
E(T)=

\square minutes
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
Calculate the expected value of the time Kelsie spends filling out daily sales reports using the probabilities and corresponding times
step 2
Multiply each time by its corresponding probability: 0×0.300 \times 0.30, 10×0.5010 \times 0.50, 20×0.1520 \times 0.15, and 30×0.0530 \times 0.05
step 3
Add the products to find the expected value: 0×0.30+10×0.50+20×0.15+30×0.050 \times 0.30 + 10 \times 0.50 + 20 \times 0.15 + 30 \times 0.05
step 4
Perform the calculations: 0+5+3+1.50 + 5 + 3 + 1.5
step 5
Sum the results to get the final expected value: 5+3+1.5=9.55 + 3 + 1.5 = 9.5 minutes
[1] Answer
9.5 minutes
Key Concept
Expected Value of a Random Variable
Explanation
The expected value is calculated by summing the products of each outcome's value and its probability. It represents the average outcome if the experiment were repeated many times.

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