Suppose it is your job to catch bottles that are underfilled by the machine. The

Question

Suppose it is your job to catch bottles that are underfilled by the machine. The machine is known to produce underfilled bottles at a rate of 3 per hour. On this particular shift, you work 4 hours.

a) If X represents the number of underfilled bottles produced during your shift, what is the distribution of X?

b) Find the probability that more than 15 underfilled bottles are produced during your shift.

c) If T represents the time until an underfilled bottle is produced during your shift, what is the distribution of T?

Explanation / Answer

a) 3 underfilled bottle per hour and hence 12 in 4 hour

X follow poisson distribution with mean = 12

b)

P(X > 15)

= 0.155584

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