Question

Record: 0/3 Score: o Penalty: 1 offComplete: 0%Saniya HallExpected ValueMar 07, 9:58:18 AM?Jacob owns a small business selling bagels. He knows that in the last week 65customers paid cash, 26 customers used a debit card, and 8 customers used a creditcard.If next week, he is expecting 600 customers, about how many would you expect topay with a credit card? Round your answer to the nearest whole number.Answer:Submit Answerattempt 1 out of 2LO

Answer 1

Solution:

Given:

$\begin{gathered} \text{cash}=65 \\ \text{debit card=26} \\ \text{credit card=8} \\ \\ \text{Total customers for the w}eek=99 \\ \\ \text{Expected value for the following we}ek=600 \end{gathered}$

To get the expected value that will pay with a credit card the following week, we use the expected value formula.

$\begin{gathered} E(x)=x.P(x) \\ \\ \text{where} \\ E(x)\text{ is the expected value} \\ x\text{ is the total expected=600} \\ P(x)\text{ is the probability} \end{gathered}$

For credit card customers, the probability for the past week was;

$P(x)=\frac{8}{99}$

Hence, the expected value for the following week will be;

$\begin{gathered} E(x)=x.P(x) \\ E(x)=600\times\frac{8}{99} \\ E(x)=\frac{4800}{99} \\ E(x)=48.48 \\ \\ To\text{ the nearest whole number,} \\ E(x)=48 \end{gathered}$

Therefore, to the nearest whole number, Jacob will expect 48 customers to pay with a credit card the following week.