Question

Math

Posted 4 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 $B=$ 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
```

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Answer from Sia

Posted 4 months ago

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 $0.30$: $0 \times 0.30 = 0$

step 3

For $B=1$ bicycle sold, $T=10$ minutes, and the probability is $0.50$: $10 \times 0.50 = 5$

step 4

For $B=2$ bicycles sold, $T=20$ minutes, and the probability is $0.15$: $20 \times 0.15 = 3$

step 5

For $B=3$ bicycles sold, $T=30$ minutes, and the probability is $0.05$: $30 \times 0.05 = 1.5$

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.

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