Last month your company sold 10,000 new watches. Past experience indicates that

Question

Last month your company sold 10,000 new watches. Past experience indicates that the probability that a new watch will need repair during its warranty period is 0.002. Let X = {number of watches which need warranty work}. (a) What probability distribution might provide a reasonable model for X? (b) Evaluate an approximation to the probability that zero watches will need warranty work. (c) Evaluate an approximation to the probability that more than 10 watches will need warranty work. (d) Evaluate an approximation to the probability that no more than 20 watches will need warranty work.

Explanation / Answer

x : Number of watches which need warranty work.

n = 10,000 , P = 0.002

a) Distribution of x is Binomial with parameter n=10000 and P = 0.002

b)

P(Zero watches need warranty work ) = P( x = 0 )

Using Excel Function.

=BINOMDIST(0,10000,0.002,0) = 0.0000

Probability that Zero watches need warranty work is zero.

c)

P( More than 10 watches will need warranty work ) = P( x > 10 )

P( x > 10 ) = 1 - P( x <= 10 )

Using Excel,

=1 - BINOMDIST(10,10000,0.002,1)= 0.9892

Probability that more than 10 watches will need warranty work is 0.9892

d)

P( no more than 20 watches will need warranty work ) = P( x <= 20 )

Using Excel,

=BINOMDIST(20,10000,0.002,1) = 0.5591

Probability that no more than 20 watches will need warranty work is 0.5591.

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