Concept explainers
A local hardware store has a “Savings Wheel” at the checkout. Customers get to spin the wheel and. when the wheel stops, a pointer indicates how much they will save. The wheel can stop in any one of 50 sections. Of the sections, 10 produce 0% off, 20 sections are for 10%off, 10 sections for 20%, 5 for 30%, 3 for 40%, 1 for 50%, and 1 for 100% off. Assuming that all 50 sections are equally likely,
- a. What is the
probability that a customer's purchase will be free (100% off)? - b. What is the probability that a customer will get no savings from the wheel (0% off)?
- c. What is the probability that a customer will get at least 20% off?
(a)
To find: The probability that a customer’s purchase will be free (100% off).
Answer to Problem 1P
The probability that a customer’s purchase will be free (100% off) is 0.02.
Explanation of Solution
Given info:
The information is based on the “savings wheel”. Customer can get to spin the wheel after it stops, a pointer indicates how much they will save.
The wheel have 50 sections. In that 10 produce 0% off, 20 produce 10% off, 10 produce 20% off, 5 produce 30% off, 3 produce 40% off, 1 produce 50% off and 1 produce 100% off.
Calculation:
The formula for probability is,
The probability that a customer’s purchase will be free (100% off) is,
Thus, the probability value is 0.02.
(b)
To find: The probability that the number of sections that a customer’s will get no savings from the wheel (0 % off).
Answer to Problem 1P
The probability that the number of sections that a customer’s will get no savings from the wheel (0 % off) is 0.2.
Explanation of Solution
Calculation:
Calculating the probability that the number of sections that a customer’s will get no savings from the wheel (0 % off) is,
Thus, the probability is 0.2.
(c)
To find: The probability that a customer will get at least 20% off.
Answer to Problem 1P
The probability that a customer will get at least 20% off is 0.40.
Explanation of Solution
Calculation:
The probability that a customer will get at least 20% off is,
Calculating the individual probability values:
For 20:
For 30:
For 40:
For 50:
For 100:
Therefore, the required probability is,
Thus, the probability value is 0.40.
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Chapter 6 Solutions
Essentials of Statistics for the Behavioral Sciences