Question

At a fast food restaurant, customers are asked if they want to “round up” their bill to the next highest        dollar and donate the additional money to charity. The cashier is instructed to tell the customer that        their bill is X dollars and Y cents. Assume that the values of Y are equally likely to be any value from 0        to 99 cents and that customers are equally likely to “round up” regardless of the amount of their bill.       The density curve below models Y, the donation amount. (a) What is the shape of the distribution of donations?   (b) What proportion of donations are at least 85 cents?   (c) What percent of donations are between 30 and 40 cents?​

Answer 1

Answer:

(a) 0.1414

(b) 0.1010

Step-by-step explanation:

(a)

The density curve is rectangular in shape.

This implies that the distribution of donations is Uniform.

(b)

Compute the probability of donations at least 85 cents as follows:

$P(X\geq 85)=\int\limits^{99}_{85} {\frac{1}{99-0} \, dx$

                 $=\frac{1}{99}\times [x]^{99}_{85}\\\\=\frac{99-85}{99}\\\\=0.1414$

Thus, the proportion of donations that are at least 85 cents is 0.1414.

(b)

Compute the probability of donations between 30 and 40 cents as follows:

$P(30\leq X\leq 40)=\int\limits^{40}_{30} {\frac{1}{99-0}} \, dx$

                         $=\frac{1}{99}\times [x]^{40}_{30}\\\\=\frac{40-30}{99}\\\\=0.1010$

Thus, the probability of donations between 30 and 40 cents is 0.1010.