A retailer is receiving a large shipment of media players. In order to determine

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Answered question

2021-09-28

A retailer is receiving a large shipment of media players. In order to determine whether she should accept or reject the shipment, she tests a sample of media players; if she finds at least one defective player, she will reject the entire shipment. If 0.5% of the media players are defective, what is the probability that she will reject the shipment if
a)she tests fifteen media players.
b)she tests thirty media players.

Answer & Explanation

SchepperJ

SchepperJ

Skilled2021-09-29Added 96 answers

Step 1
Given:
p=0.5%=0.005
Step 2
a) n=15
Using binomial probability formula
P(X=x)=nCx×px×(1p)nx
P(X1)=1P(X=0)
=115C0×(0.005)0×(0.995)15
=11×1×0.92756
=0.07244
The probability that she will reject the shipment if she tests fifteen media players is 0.07244
Step 3
b) n=30
Using binomial probability formula
P(X=x)=nCx×px×(1p)nx
P(X1)=1P(X=0)
=130C0×(0.005)0×(0.995)30
=11×1×0.86038
=0.13962
The probability that she will reject the shipment if she tests thirty media players is 0.13962

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