Recent statistics suggest that 15% of those who visit a retail site on the World Wide Web make a purchase. A retailer wished to verify this claim. To do so, she selected a sample of 16 "hits" to her site and found that 4 had actually made a purchase. a. What is the likelihood of exactly four purchases? (Round your answer to 4 decimal places.)     b. How many purchases should she expect? (Round your answer to 1 decimal place.)     c. What is the likelihood that four or more "hits" result in a purchase? (Round your answer to 2 decimal places.)

Question
Asked Oct 16, 2019

Recent statistics suggest that 15% of those who visit a retail site on the World Wide Web make a purchase. A retailer wished to verify this claim. To do so, she selected a sample of 16 "hits" to her site and found that 4 had actually made a purchase.

 

a. What is the likelihood of exactly four purchases? (Round your answer to 4 decimal places.)

 

 

 

 

 

b. How many purchases should she expect? (Round your answer to 1 decimal place.)

 

 

 

 

 

c. What is the likelihood that four or more "hits" result in a purchase? (Round your answer to 2 decimal places.)

 

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Expert Answer

Step 1

(a)

The likelihood of exactly four purchases is,

(p)
P(X x)
|P" (1- р)"*
P(X 4).15'(-0.15)
=0.1311
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(p) P(X x) |P" (1- р)"* P(X 4).15'(-0.15) =0.1311

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Step 2

Thus, the likelihood of exactly four purchases is 0.1311.

(b)

The number of purchases should she expect is,

=np
=16(0.15)
- 2.4
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=np =16(0.15) - 2.4

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Step 3

Thus, the number purchases should she expect is 2.4.

(c)

The likelihood that fou...

п
P(Xx) -p)
х
P(X2 4) 1-P(X < 4)
=1-{P(X 0)+ P(X = 1)+ P(X 2)+ P(X =3)}
(C9)
16
16
0.15'(1-0.15)
16-0
16-1
0
1-
16
0.15 (1-0.15)
16-3
3
=1-0.79
=0.21
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п P(Xx) -p) х P(X2 4) 1-P(X < 4) =1-{P(X 0)+ P(X = 1)+ P(X 2)+ P(X =3)} (C9) 16 16 0.15'(1-0.15) 16-0 16-1 0 1- 16 0.15 (1-0.15) 16-3 3 =1-0.79 =0.21

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