type of photocopier has a paper Jam on average once every 3000 copies. What is the probability that there will be more than two jams in a 3000 copy run

The problem can be solved using the Poisson distribution, which is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.

The formula for the Poisson distribution is:

P(x; μ) = (e^-μ) * (μ^x) / x!

where:

• P(x; μ) is the probability of x events in an interval,
• e is the base of the natural logarithm (approximately equal to 2.71828),
• μ is the average rate of value (in this case, 1, because on average there is 1 jam per 3000 copies),
• x is the actual number of successes that result from the experiment (in this case, we want to find the probability of more than 2 jams, so we need to calculate the probability for x=0, x=1, and x=2, and then subtract these from 1 to find the probability of more than 2 jams).

Step 1: Calculate P(x=0; μ=1) P(0; 1) = (e^-1) * (1^0) / 0! = 0.3679

Step 2: Calculate P(x=1; μ=1) P(1; 1) = (e^-1) * (1^1) / 1! = 0.3679

Step 3: Calculate P(x=2; μ=1) P(2; 1) = (e^-1) * (1^2) / 2! = 0.1839

Step 4: Calculate the probability of more than 2 jams P(x>2; μ=1) = 1 - P(0; 1) - P(1; 1) - P(2; 1) = 1 - 0.3679 - 0.3679 - 0.1839 = 0.0803

So, the probability that there will be more than two jams in a 3000 copy run is approximately 0.0803, or 8.03%.