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Chapter 5: Q 5.94. (page 217)

Sale tax receipts. Refer to exercise 5.88. Use the complementation rule to find the probability that one of these type 4A development corporation selected at random has receipts

Part (a) of at least \(25,000

Part (b) less than \)500,000

Short Answer

Expert verified

Part (a) =182207

Part (b)=158207

Step by step solution

01

Part (a) Step 1. Given information.

The sales tax receipts from the state's Type 4A development corporations for one fiscal year are summarised in the frequency distribution below:

ReceiptsFrequency
$0-24,99925
$25,000-49,99923
$50,000-74,99921
$75,000-99,99911
$100,000-199,99934
$200,000-499,99944
$500,000-999,99917
$1,000,000& over32

A = receipts are less than $25,000,

B = receipts are between $25,000 and $49,999,

C= receipts are between $500,000 and $999,999,

D = receipts are at least $1,000,000, and

R = receipts are either less than $50,000 or at least $500,000.

02

Part (a) Step 2. To determine the likelihood that one of these Type 4A development businesses, chosen at random, has at least $25,000 in receipts.

Assume that you have at least $25,000 in receipts.

E =not( A)

Using complement鈥檚 rule:

P(E)=1-P(A)P(E)=1-25207P(E)=182207

03

Part (b) Step 1.  The chance that one of the Type 4A development corporations chosen at random has receipts of less than $500,000.

Let E1represent the case where the total revenue is less than $500,000.

E1=not(CorD)

Using complement鈥檚 rule:

P(E1)=1-(P(C)+P(D))P(E1)=1-17207+32207P(E1)=1-49207P(E1)=158207

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