Question

for parts (a) and (b) below, choose the correct description.
(a) a local store in keeping track of service times. the table below shows the number of customers served and the time it took.
number of customers
time (in minutes)
3
9
4
12
9
27
choose the correct description.
it does not always take the same amount of time to serve each customer.
it appears to take the same amount of time to serve each customer.
predicted number of customers served in 30 minutes:
(b) customers of a certain credit card earn points for using the card. the table below shows the number of points earned for the amount spent.
number of points
dollars spent
36
4
56
7
72
9
choose the correct description.
each dollar spent does not always earn the same number of points.
each dollar spent appears to earn the same number of points.
predicted number of points for spending $10:

Explanation:

Part (a)

Step1: Calculate time per customer

For the first row: $\frac{9}{3}=3$ minutes per customer.
For the second row: $\frac{12}{4}=3$ minutes per customer.
For the third row: $\frac{27}{9}=3$ minutes per customer.
Since the time per customer is constant ($3$ minutes), it appears to take the same amount of time to serve each customer.

Part (b)

Step1: Find points per dollar

For the first row: $\frac{36}{4}=9$ points per dollar.
For the second row: $\frac{56}{7}=8$ points per dollar.
For the third row: $\frac{72}{9}=8$ points per dollar.
Since the points per dollar are not the same (first row is $9$, others are $8$), each dollar spent does not always earn the same number of points.

Step2: Predict points for $10$ dollars

We can use the majority rate (since two out of three rows have $8$ points per dollar). For $10$ dollars, the predicted number of points is $10\times8 = 80$.

Answer:

(a) It appears to take the same amount of time to serve each customer.
(b) Predicted number of points for spending $\$10$: $80$