Chapter 8.1, Problem 8.19E

(a)

To determine

To calculate $P(X<\$0.10)$ and interpret your result.

Answer to Problem 8.19E

  $15.15\%$ of all people will pay less than $0.10$ for an ice cream.

Explanation of Solution

Add all the corresponding probabilities:

  $\begin{array}{l}P(X<\$0.10)=P(X=0)+P(X=0.01)+P(X=0.02)+P(X=0.09)\\ =\frac{5}{132}+\frac{5}{132}+\frac{5}{132}+\frac{5}{132}\\ =0.1515\\ =15.15\%\end{array}$

Thus about $15.15\%$ of all people will pay less than $0.10$ for an ice cream.

(b)

To determine

To calculate the probability that Mary will pay less than the usual cost of an ice cream bar and also write this probability in terms of random variable X .

Answer to Problem 8.19E

  $34.09\%$ of all people will pay less than the usual cost for an ice cream.

Explanation of Solution

Add all the corresponding probabilities:

  $\begin{array}{l}P(X<\$0.40)=P(X=0)+P(X=0.01)+P(X=0.02)+P(X=0.09)+P(X=0.20)+P(X=0.34)\\ =\frac{5}{132}+\frac{5}{132}+\frac{5}{132}+\frac{5}{132}+\frac{10}{132}+\frac{15}{132}\\ =\frac{45}{132}\\ =0.3409\\ =34.09\%\end{array}$

Thus about $34.09\%$ of all people will pay less than the usual cost for an ice cream.

(c)

To determine

To calculate how much money will the store take in if all the balloons are popped and also how much would the store have made on these ice cream bars without the promotion.

Answer to Problem 8.19E

Amount of money made if all balloons are popped: $\$43.96$

Amount of money made without promotions: $\$52.80$ .

Explanation of Solution

Amount of money made if all balloons are popped:

  $\begin{array}{l}30\times \$0.43+18\times \$0.42+20\times \$0.41+19\times \$0.40+15\times \$0.34+10\times \$0.20+5\times \$0.09\\ +5\times \$0.02+5\times \$0.01+5\times \$0\\ =\$43.96\end{array}$

Amount of money made without promotions:

  $132\times \$0.40=\$52.80$

Thus we note that the different is $6.69$ and thus this is the amount of profit they loose due to the promotion.