A IT distribution company in Hong Kong gives a bonus to salespeople that generate more than HK$180,000 in a single day. On average this happens 5% of the time. If the company employs 20 salespeople, what is the probability of paying exactly 1 bonus on any particular day (give as a percentage, 0 decimal places)?
A) 37%
B) 38%
C) 39%
D) 40%

Question

Quizplus · Accepted Answer

The probability of exactly 1 salesperson out of 20 generating more than HK$180,000 in a single day, and thus earning a bonus, can be calculated using the binomial probability formula. The formula for exactly k successes (in this case, 1 bonus) out of n trials (in this case, 20 salespeople) is given by:$$ P(k; n, p) = \binom{n}{k} p^k (1-p)^{n-k} $$where $\binom{n}{k}$ is the binomial coefficient, $p$ is the probability of success on a single trial (5% or 0.05), and $1-p$ is the probability of failure on a single trial.For exactly 1 bonus:$$ P(1; 20, 0.05) = \binom{20}{1} (0.05)^1 (0.95)^{19} $$$$ P(1; 20, 0.05) = 20 \times 0.05 \times (0.95)^{19} $$$$ P(1; 20, 0.05) \approx 0.377 $$$$ P(1; 20, 0.05) \approx 38\% $$Therefore, the probability of paying exactly 1 bonus on any particular day is approximately 38%.

A IT Distribution Company in Hong Kong Gives a Bonus