A small post-production company re-masters soundtracks for movies and television

Question

A small post-production company re-masters soundtracks for movies and television shows, through a process that tries to minimize reading errors on the final master DVD copy. This population of master DVDs will have errors that are normally distributed, with a mean of µ = 3.5 errors/DVD and a standard deviation of s = 1.75 errors / DVD.

If Screen Green Productions contracts post-production for 14 films with this company, what is the probability that Screen Green Productions will experience on average no more than 2 errors / DVD?


Probability=
(Express your answer in decimal form and round your final answer to four decimal places)

Explanation / Answer

Given n=14, X~Normal(µ = 3.5, s=1.75)

So the probability is
P(X<=2) = P((X-)/(s/n) <=(2-3.5)/(1.75/sqrt(14)))

=P(Z<=-3.21 )

= 0.00066 (check standard normal table)

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