Math

StatisticsEssentials of Statistics for the Behavioral SciencesA 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?BuyFind*launch*

8th Edition

Frederick J Gravetter + 1 other

Publisher: Cengage Learning

ISBN: 9781133956570

Chapter 6, Problem 1P

Textbook Problem

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?

Expert Solution

**(a)**

To determine

**To find:** The probability that a customer’s purchase will be free (100% off).

The probability that a customer’s purchase will be free (100% off) is 0.02.

**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.

Expert Solution

**(b)**

To determine

**To find:** The probability that the number of sections that a customer’s will get no savings from the wheel (0 % off).

The probability that the number of sections that a customer’s will get no savings from the wheel (0 % off) is 0.2.

**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.

Expert Solution

**(c)**

To determine

**To find:** The probability that a customer will get at least 20% off.

The probability that a customer will get at least 20% off is 0.40.

**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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Essentials of Statistics for the Behavioral Sciences

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