A corner shop compares complaint rates for two snack suppliers over the same month. The table shows the number of deliveries and the number of complaints fo...
Question 1 Report
A corner shop compares complaint rates for two snack suppliers over the same month. The table shows the number of deliveries and the number of complaints for each.
| Supplier | Deliveries | Complaints |
|---|---|---|
| P | 40 | 6 |
| Q | 25 | 5 |
- Estimate the probability that a delivery from Supplier P results in a complaint. (1)
- Estimate the probability for Supplier Q. (1)
- The shop can keep only one supplier. Using your answers, decide which one, giving a reason. (1)
- Next month it expects \(60\) deliveries from the chosen supplier. Estimate the number of complaints expected. (2)
- State one assumption made in part (d). (1)
Answer Details
A complaint rate is estimated from past data as (number of complaints) \(\div\) (number of deliveries); comparing two such rates identifies the more reliable supplier, and multiplying the chosen rate by a future number of deliveries estimates future complaints, assuming the rate stays constant.
(a) Supplier P's rate: \(6\div40 = 0.15\). [1 mark]
(b) Supplier Q's rate: \(5\div25 = 0.2\). [1 mark]
(c) Since \(0.15 \lt 0.2\), Supplier P has the lower complaint rate, so the shop should keep Supplier P. [1 mark]
(d) Applying Supplier P's rate to 60 expected deliveries: \(0.15\times60 = 9\) complaints expected. [2 marks]
(e) This estimate assumes Supplier P's complaint rate next month stays the same as it was this month. [1 mark]
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