Recent statistics suggest that 15 percent of those who visit a retail site on th

Question

Recent statistics suggest that 15 percent 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.)

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a.
the likelihood of exactly four purchases = P( X = 4 ) = ( 16 4 ) * ( 0.15^4) * ( 1 - 0.15 )^12
= 0.1311

b.
purchases should she expect = Mean ( np ) =16 * 0.15 = 2.4

c.

P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 16 3 ) * 0.15^3 * ( 1- 0.15 ) ^13 + ( 16 2 ) * 0.15^2 * ( 1- 0.15 ) ^14 + ( 16 1 ) * 0.15^1 * ( 1- 0.15 ) ^15 + ( 16 0 ) * 0.15^0 * ( 1- 0.15 ) ^16
= 0.7899
P( X > = 4 ) = 1 - P( X < 4) = 0.2101          

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