Interpret the Mean of a Discrete Random Variable as an Expected Value
-A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. The distribution is as follows:
$\begin{array}{l|ccccc}
\text { Number sold in a day } & 0 & 5 & 10 & 15 & 20 \
\hline \text { Prob (Number sold) } & 0.1 & 0.15 & 0.19 & 0.16 & 0.4
\end{array}$

Find the number of cheesecakes that this local bakery expects to sell in a day.
A) $13.05$
B) $13.15$
C) $13.55$
D) 10

Question

Interpret the Mean of a Discrete Random Variable as an Expected Value
-A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. The distribution is as follows:
$\begin{array}{l|ccccc}
\text { Number sold in a day } & 0 & 5 & 10 & 15 & 20 \
\hline \text { Prob (Number sold) } & 0.1 & 0.15 & 0.19 & 0.16 & 0.4
\end{array}$

Find the number of cheesecakes that this local bakery expects to sell in a day.
A) $13.05$
B) $13.15$
C) $13.55$
D) 10

Quizplus · Accepted Answer

The expected value (mean) of a discrete random variable is calculated by multiplying each possible value by its probability and then summing these products. For the given distribution: $E(X) = 0*0.1 + 5*0.15 + 10*0.19 + 15*0.16 + 20*0.4 = 0 + 0.75 + 1.9 + 2.4 + 8 = 13.05$.