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 $B=$ the number of bicycles Kelsie sells on a randomly selected day, and $T=$ the time she spends filling out daily sales reports.
\begin{tabular}{lcccc}
\hline$B=$ \# of bicycles sold & 0 & 1 & 2 & 3 \
$T=$ 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.
$$
E(T)=
$$
$\square$ minutes

Question

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 $B=$ the number of bicycles Kelsie sells on a randomly selected day, and $T=$ the time she spends filling out daily sales reports.
\begin{tabular}{lcccc}
\hline$B=$ \# of bicycles sold & 0 & 1 & 2 & 3 \
$T=$ 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.
$$
E(T)=
$$
$\square$ minutes

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the expected value of time spent on reports by multiplying each time value by its corresponding probability. ‖ ‖ step 2 ⋮ For $B=0$ bicycles sold, $T=0$ minutes, and the probability is $0.30$: $0 imes 0.30 = 0$. ‖ ‖ step 3 ⋮ For $B=1$ bicycle sold, $T=10$ minutes, and the probability is $0.50$: $10 imes 0.50 = 5$. ‖ ‖ step 4 ⋮ For $B=2$ bicycles sold, $T=20$ minutes, and the probability is $0.15$: $20 imes 0.15 = 3$. ‖ ‖ step 5 ⋮ For $B=3$ bicycles sold, $T=30$ minutes, and the probability is $0.05$: $30 imes 0.05 = 1.5$. ‖ ‖ step 6 ⋮ Add the results of steps 2 to 5 to find the expected value: $0 + 5 + 3 + 1.5 = 9.5$. ‖ ∻Answer∻ ⚹ The expected value of the amount of time Kelsie spends filling out daily sales reports is 9.5 minutes. ⚹ ∻Key Concept∻ ⚹Expected Value⚹ ∻Explanation∻ ⚹The expected value of a random variable is calculated by summing the products of each outcome with its corresponding probability.⚹◊What is the formula to calculate the expected value E(T) of the time Kelsie spends filling out daily sales reports?⍭ Generate me a similar question◊

Sia