   Chapter 6, Problem 1P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
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?

(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.

Explanation

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,

p(A)= Number of outcomes classified as A      Total number of possible outcomes

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

p(A)=(The number of sections that a customer's purchase will be free (100% off ))  Total number of sections =150  =0.02

Thus, the probability value is 0.02.

(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.

Explanation

Calculation:

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

p(B)=(The number of sections that a customer's will get no savings from the wheel (0% off))  Total number of sections =1050=15=0.2

Thus, the probability is 0.2.

(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.

Explanation

Calculation:

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

p(X20%)=p(X=20%)+p(X=30%)+p(X=40%)                       +p(X=50%)+p(X=100%)

Calculating the individual probability values:

For 20:

p(X=20%)=(The number of sections that a customer's purchase will be 20% off)  Total number of sections      =1050

For 30:

p(X=30%)=(The number of sections that   a customer's purchase will be 30% off)  Total number of sections =550

For 40:

p(X=40%)=(The number of sections that a customer's purchase will be 40% off)  Total number of sections =350

For 50:

p(X=50%)=(The number of sections thata customer's purchase will be 50% off)  Total number of sections =150

For 100:

p(X=100%)=(The number of sections that   a customer's purchase will be 100% off)  Total number of sections =150

Therefore, the required probability is,

p(X20%)=1050+550+350+150+150=2050=0.40

Thus, the probability value is 0.40.

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