Question

The Securities and Exchange Commission has determined that the number of companies listed in NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that exactly 4 bankruptcies occur next month?

1) .8774
2) .1414
3) .1557
4) .2176

Answer 1

3) .1557

To find the probability that exactly 4 bankruptcies occur next month, use the Poisson distribution formula. The probability is approximately 0.1557.

Step-by-step explanation:

The given problem can be solved using the Poisson distribution formula. In this case, we have a mean of 2.6 bankruptcies per month. The formula for the probability mass function (PMF) of a Poisson distribution is:

P(X = k) = (e^-λ * λ^k) / k!

Where λ is the mean.

To find the probability that exactly 4 bankruptcies occur next month, we substitute k = 4 and λ = 2.6 into the formula:

P(X = 4) = (e^-2.6 * 2.6^4) / 4!

Calculating this probability gives us approximately 0.1557, which corresponds to option 3) .1557.