A company makes frozen dumplings which are packaged in plastic bags. Suppose tha

Question

A company makes frozen dumplings which are packaged in plastic bags. Suppose that the filling machine on the production line overfills a bag 25% of the time. Assume that hags of dumplings are overfilled independently from one another. A random sequence of bags will be examined. For parts a, b, and c, identify the distribution of the random variable and give the values of its associated parameter(s). a. U = the number of bags examined until five overfilled bag are found. b. V = the number of bags examined until an overfilled bags is found. c. W = the number of overfilled bags in the next ten bags that are examined.

Explanation / Answer

a) P(U =n) = probability of finding 4 overfilled bag in (n-1) bags and an ovefilled bag in last>

(n-1)C4 *p^4 (1-p)^(n-5)*p , here p = 0.25

where nCr =(n!/((n-r)!r!)

b) This is geometic distribution

as probability of finding no overfilled bag in (n-1) bags and an ovefilled bag in last>

=P(V =n) = (i-p)^(n-1)*p

c)this is binomial distribution

P(W=n) = 10Cn *p^n*(1-p)^(10-n)

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